Multi-Class Classification Model for Human Activities and Postural Transitions Using R Take 1
David Lowe
February 1, 2019
Template Credit: Adapted from a template made available by Dr. Jason Brownlee of Machine Learning Mastery. [https://machinelearningmastery.com/]
SUMMARY: The purpose of this project is to construct a prediction model using various machine learning algorithms and to document the end-to-end steps using a template. The Human Activities and Postural Transitions dataset is a classic multi-class classification situation where we are trying to predict one of the 12 possible outcomes.
INTRODUCTION: The research team carried out experiments with a group of 30 volunteers who performed a protocol of activities composed of six basic activities. There are three static postures (standing, sitting, lying) and three dynamic activities (walking, walking downstairs and walking upstairs). The experiment also included postural transitions that occurred between the static postures. These are stand-to-sit, sit-to-stand, sit-to-lie, lie-to-sit, stand-to-lie, and lie-to-stand. All the participants were wearing a smartphone on the waist during the experiment execution. The research team also video-recorded the activities to label the data manually. The research team randomly partitioned the obtained data into two sets, 70% for the training data and 30% for the testing.
In the current iteration Take1, the script will focus on evaluating various machine learning algorithms and identifying the model that produces the best overall metrics. Because the dataset has many attributes that are collinear with other attributes, we will eliminate the attributes that have a collinearity measurement of 99% or higher. Iteration Take1 will establish the baseline performance for accuracy and processing time.
ANALYSIS: In the current iteration Take1, the baseline performance of the machine learning algorithms achieved an average accuracy of 89.61%. Two algorithms (Linear Discriminant Analysis and Stochastic Gradient Boosting) achieved the top accuracy metrics after the first round of modeling. After a series of tuning trials, Stochastic Gradient Boosting turned in the top overall result and achieved an accuracy metric of 97.70%. By using the optimized parameters, the Stochastic Gradient Boosting algorithm processed the testing dataset with an accuracy of 92.85%, which was below the training data and possibly due to over-fitting.
From the model-building perspective, the number of attributes decreased by 108, from 561 down to 453.
CONCLUSION: For this iteration, the Stochastic Gradient Boosting algorithm achieved the best overall results. For this dataset, we should consider using the Stochastic Gradient Boosting algorithm for further modeling or production use.
Dataset Used: Smartphone-Based Recognition of Human Activities and Postural Transitions Data Set
Dataset ML Model: Multi-class classification with numerical attributes
Dataset Reference: https://archive.ics.uci.edu/ml/datasets/Smartphone-Based+Recognition+of+Human+Activities+and+Postural+Transitions
The project aims to touch on the following areas:
- Document a predictive modeling problem end-to-end.
- Explore data cleaning and transformation options
- Explore non-ensemble and ensemble algorithms for baseline model performance
- Explore algorithm tuning techniques for improving model performance
Any predictive modeling machine learning project genrally can be broken down into about six major tasks:
- Prepare Problem
- Summarize Data
- Prepare Data
- Model and Evaluate Algorithms
- Improve Accuracy or Results
- Finalize Model and Present Results
1. Prepare Problem
1.a) Load libraries
startTimeScript <- proc.time()
library(caret)## Loading required package: lattice## Loading required package: ggplot2library(corrplot)## corrplot 0.84 loadedlibrary(mailR)
library(stringr)
library(MLmetrics)##
## Attaching package: 'MLmetrics'## The following objects are masked from 'package:caret':
##
## MAE, RMSE## The following object is masked from 'package:base':
##
## Recalllibrary(DMwR)## Loading required package: gridlibrary(mlbench)
# Create one random seed number for reproducible results
seedNum <- 888
set.seed(seedNum)1.b) Set up the email notification function
email_notify <- function(msg=""){
sender <- "luozhi2488@gmail.com"
receiver <- "dave@contactdavidlowe.com"
sbj_line <- "Notification from R Multi-Class Classification Script"
password <- readLines("../email_credential.txt")
send.mail(
from = sender,
to = receiver,
subject= sbj_line,
body = msg,
smtp = list(host.name = "smtp.gmail.com", port = 465, user.name = sender, passwd = password, ssl = TRUE),
authenticate = TRUE,
send = TRUE)
}email_notify(paste("Library and Data Loading has begun!",date()))## [1] "Java-Object{org.apache.commons.mail.SimpleEmail@3c0f93f1}"1.c) Load dataset
widthVector <- rep(16, 561)
colNames <- paste0("attr",1:561)
x_train <- read.csv("X_train.txt", header = FALSE, col.names = colNames, sep = " ")
y_train <- read.csv("Y_train.txt", header = FALSE, col.names = c("targetVar"))
y_train$targetVar <- as.factor(y_train$targetVar)
xy_train <- cbind(x_train, y_train)
x_test <- read.csv("X_test.txt", header = FALSE, col.names = colNames, sep = " ")
y_test <- read.csv("Y_test.txt", header = FALSE, col.names = c("targetVar"))
y_test$targetVar <- as.factor(y_test$targetVar)
xy_test <- cbind(x_test, y_test)# Use variable totCol to hold the number of columns in the dataframe
totCol <- ncol(xy_train)
# Set up variable totAttr for the total number of attribute columns
totAttr <- totCol-11.d) Set up the key parameters to be used in the script
# Set up the number of row and columns for visualization display. dispRow * dispCol should be >= totAttr
dispCol <- 5
if (totAttr%%dispCol == 0) {
dispRow <- totAttr%/%dispCol
} else {
dispRow <- (totAttr%/%dispCol) + 1
}
cat("Will attempt to create graphics grid (col x row): ", dispCol, ' by ', dispRow)## Will attempt to create graphics grid (col x row): 5 by 1131.e) Set test options and evaluation metric
# Run algorithms using 10-fold cross validation
control <- trainControl(method="repeatedcv", number=10, repeats=1)
metricTarget <- "Accuracy"email_notify(paste("Library and Data Loading completed!",date()))## [1] "Java-Object{org.apache.commons.mail.SimpleEmail@a67c67e}"2. Summarize Data
To gain a better understanding of the data that we have on-hand, we will leverage a number of descriptive statistics and data visualization techniques. The plan is to use the results to consider new questions, review assumptions, and validate hypotheses that we can investigate later with specialized models.
email_notify(paste("Data Summarization and Visualization has begun!",date()))## [1] "Java-Object{org.apache.commons.mail.SimpleEmail@5ec0a365}"2.a) Descriptive statistics
2.a.i) Peek at the data itself.
head(xy_train)## attr1 attr2 attr3 attr4 attr5 attr6
## 1 0.04357967 -0.005970221 -0.03505434 -0.9953812 -0.9883659 -0.9373820
## 2 0.03948004 -0.002131276 -0.02906736 -0.9983480 -0.9829449 -0.9712729
## 3 0.03997778 -0.005152716 -0.02265071 -0.9954821 -0.9773138 -0.9847595
## 4 0.03978456 -0.011808778 -0.02891578 -0.9961941 -0.9885686 -0.9932556
## 5 0.03875814 -0.002288533 -0.02386289 -0.9982413 -0.9867741 -0.9931155
## 6 0.03898801 0.004108852 -0.01734026 -0.9974376 -0.9934854 -0.9966920
## attr7 attr8 attr9 attr10 attr11 attr12
## 1 -0.9950070 -0.9888156 -0.9533252 -0.7947964 -0.7448928 -0.6484472
## 2 -0.9987020 -0.9833148 -0.9739998 -0.8025366 -0.7363378 -0.7124148
## 3 -0.9964148 -0.9758348 -0.9859730 -0.7984772 -0.7363378 -0.7124148
## 4 -0.9969943 -0.9885264 -0.9931354 -0.7984772 -0.7527779 -0.7221857
## 5 -0.9982159 -0.9864792 -0.9938246 -0.8019815 -0.7465054 -0.7178581
## 6 -0.9975222 -0.9934935 -0.9969160 -0.8019815 -0.7433715 -0.7161817
## attr13 attr14 attr15 attr16 attr17 attr18
## 1 0.8417956 0.7084402 0.6517165 -0.9757520 -0.9999502 -0.9998884
## 2 0.8387581 0.7084402 0.6593403 -0.9874270 -0.9999927 -0.9998263
## 3 0.8340019 0.7050081 0.6745507 -0.9885282 -0.9999725 -0.9997194
## 4 0.8340019 0.7050081 0.6732080 -0.9903894 -0.9999784 -0.9997827
## 5 0.8385806 0.7058541 0.6732080 -0.9950571 -0.9999921 -0.9998824
## 6 0.8385806 0.7181487 0.6805388 -0.9959641 -0.9999874 -0.9998833
## attr19 attr20 attr21 attr22 attr23 attr24
## 1 -0.9980137 -0.9939993 -0.9919796 -0.9709701 -0.5470954 -0.7009736
## 2 -0.9994107 -0.9989183 -0.9854825 -0.9734814 -0.7819734 -0.5346039
## 3 -0.9998026 -0.9968982 -0.9767812 -0.9867541 -0.6881761 -0.5205140
## 4 -0.9998152 -0.9969486 -0.9894371 -0.9924404 -0.7151026 -0.8609883
## 5 -0.9999083 -0.9977723 -0.9877261 -0.9951089 -0.8367735 -0.5892004
## 6 -0.9999675 -0.9973519 -0.9948008 -0.9971607 -0.8102506 -0.4915608
## attr25 attr26 attr27 attr28 attr29 attr30
## 1 -0.6226971 0.9218842 -0.71948288 0.3421680 -0.16131765 0.26604897
## 2 -0.5931648 0.6074353 -0.26678274 0.2758824 0.20041658 0.13126564
## 3 -0.5931648 0.2722625 -0.05642431 0.3222829 -0.27329167 0.03717982
## 4 -0.9164289 0.0628164 0.08293970 0.2005662 -0.37826161 0.09006277
## 5 -0.7737707 0.3121055 -0.09525383 0.1943987 -0.00799849 0.26673995
## 6 -0.5741065 0.3881044 -0.13941549 0.1660186 0.09785734 0.26896972
## attr31 attr32 attr33 attr34 attr35 attr36
## 1 -0.2743515 0.2672051 -0.02095843 0.3826102 -0.50174806 0.51246321
## 2 -0.1490167 0.2924360 -0.19298551 0.2174964 -0.08917505 0.05990858
## 3 -0.1336120 0.3324868 -0.24049052 0.3487328 -0.19540881 0.22943640
## 4 -0.2092639 0.3165300 -0.09086207 0.3963826 -0.35364269 0.50375356
## 5 -0.3189649 0.4097313 -0.22458943 0.5203539 -0.31916749 0.23437579
## 6 -0.2915595 0.3988789 -0.31994831 0.6219899 -0.27191893 0.22167264
## attr37 attr38 attr39 attr40 attr41 attr42
## 1 -0.20633687 0.37677800 0.43517232 0.6601985 0.9600507 -0.1359387
## 2 -0.23660913 -0.01269628 -0.07271079 0.5786491 0.9632148 -0.1366480
## 3 -0.31681581 -0.12388942 -0.18113694 0.6082186 0.9635317 -0.1371051
## 4 -0.49038926 -0.30475944 -0.36270837 0.5066018 0.9642686 -0.1390654
## 5 -0.10265050 -0.15497394 -0.18979591 0.5985146 0.9648776 -0.1438237
## 6 0.07014599 -0.20911148 -0.15109212 0.1790016 0.9646015 -0.1432852
## attr43 attr44 attr45 attr46 attr47 attr48
## 1 0.11555554 -0.9881345 -0.9826928 -0.9197227 -0.9883619 -0.9855230
## 2 0.10955844 -0.9979176 -0.9900056 -0.9551601 -0.9983578 -0.9903461
## 3 0.10206233 -0.9996573 -0.9932357 -0.9953640 -0.9997170 -0.9931219
## 4 0.10002822 -0.9973016 -0.9823946 -0.9858896 -0.9972507 -0.9823173
## 5 0.09466311 -0.9987365 -0.9887307 -0.9860658 -0.9987672 -0.9894554
## 6 0.09208651 -0.9991789 -0.9874604 -0.9982436 -0.9992659 -0.9875346
## attr49 attr50 attr51 attr52 attr53 attr54
## 1 -0.9318338 0.8920545 -0.1613504 0.12465977 0.9774363 -0.1215128
## 2 -0.9567964 0.8920603 -0.1614275 0.12258573 0.9845201 -0.1132053
## 3 -0.9954374 0.8924006 -0.1637959 0.09456584 0.9867701 -0.1132053
## 4 -0.9860652 0.8938171 -0.1637959 0.09342467 0.9868211 -0.1196380
## 5 -0.9863758 0.8938171 -0.1668706 0.09168239 0.9874335 -0.1201351
## 6 -0.9983404 0.8936834 -0.1670548 0.08334712 0.9877218 -0.1201351
## attr55 attr56 attr57 attr58 attr59 attr60
## 1 0.05611428 -0.3744642 0.8918215 -0.9708356 -0.9755107 -0.9891408
## 2 0.10237952 -0.3824801 0.9001481 -0.9705123 -0.9785008 -0.9994364
## 3 0.10237952 -0.4006802 0.9009836 -0.9702972 -0.9816727 -0.9997762
## 4 0.09537050 -0.3993546 0.9029287 -0.9693264 -0.9824200 -0.9972114
## 5 0.09367780 -0.3995534 0.9045361 -0.9669723 -0.9843630 -0.9988336
## 6 0.09367780 -0.4084490 0.9038070 -0.9672424 -0.9852757 -0.9995472
## attr61 attr62 attr63 attr64 attr65 attr66 attr67
## 1 -0.9904443 -0.9488870 -1 -1 0.03424856 -0.593146212 0.59463587
## 2 -0.9914546 -0.9637786 -1 -1 -0.26688692 -0.414654102 0.41970738
## 3 -0.9932328 -0.9954574 -1 -1 -0.93200653 -0.006655758 0.03847818
## 4 -0.9834323 -0.9874714 -1 -1 -0.62495078 -0.073125639 0.08578606
## 5 -0.9919538 -0.9878656 -1 -1 -0.64396547 -0.263455687 0.27669978
## 6 -0.9884875 -0.9986352 -1 -1 -1.00000000 -0.307945770 0.38534698
## attr68 attr69 attr70 attr71 attr72 attr73
## 1 -0.59643990 0.5985603 -0.71220910 0.70963040 -0.70748448 0.70500050
## 2 -0.42506575 0.4307221 -0.09034915 0.08933676 -0.08980775 0.09027531
## 3 -0.07009309 0.1014171 -0.24059474 0.24053159 -0.24139845 0.24186914
## 4 -0.09871488 0.1118854 -0.20210338 0.19658572 -0.19232572 0.18797520
## 5 -0.29038937 0.3044995 -0.05675133 0.05246193 -0.04986365 0.04744427
## 6 -0.46407635 0.5439649 -0.09234864 0.09125391 -0.09182956 0.09259692
## attr74 attr75 attr76 attr77 attr78 attr79
## 1 -0.9921171 0.9926469 -0.9928854 0.9917479 0.5702688 0.4390651
## 2 -0.8329200 0.8332964 -0.8334545 0.8323968 -0.8312777 -0.8655856
## 3 -0.7057012 0.7149424 -0.7239782 0.7318479 -0.1810648 0.3379804
## 4 -0.3901013 0.3910961 -0.3920717 0.3922717 -0.9913072 -0.9686889
## 5 -0.2440304 0.2458628 -0.2478208 0.2492269 -0.4083119 -0.1847604
## 6 -0.1654648 0.1827825 -0.2001898 0.2169948 -0.5639370 0.4665066
## attr80 attr81 attr82 attr83 attr84 attr85
## 1 0.9869130 0.07799634 0.005000803 -0.09778959 -0.9935191 -0.9883600
## 2 0.9743853 0.07400671 0.005771104 -0.01217132 -0.9955481 -0.9810636
## 3 0.6434127 0.07363596 0.003104037 -0.04601284 -0.9907428 -0.9809556
## 4 0.9842553 0.07732061 0.020057642 -0.04673432 -0.9926974 -0.9875528
## 5 0.9647961 0.07344436 0.019121574 -0.02326619 -0.9964202 -0.9883587
## 6 0.4430904 0.07793244 0.018684046 -0.02981526 -0.9948136 -0.9887145
## attr86 attr87 attr88 attr89 attr90 attr91
## 1 -0.9935750 -0.9944374 -0.9862066 -0.9928184 -0.9851801 -0.9919942
## 2 -0.9918457 -0.9955817 -0.9789380 -0.9912766 -0.9945447 -0.9790682
## 3 -0.9896866 -0.9908828 -0.9793002 -0.9872381 -0.9870770 -0.9790682
## 4 -0.9934976 -0.9942157 -0.9857170 -0.9914832 -0.9870770 -0.9917862
## 5 -0.9924549 -0.9965471 -0.9865370 -0.9906864 -0.9969933 -0.9918178
## 6 -0.9922663 -0.9951916 -0.9868467 -0.9910667 -0.9941054 -0.9918178
## attr92 attr93 attr94 attr95 attr96 attr97
## 1 -0.9931189 0.9898347 0.9919569 0.9905192 -0.9936582 -0.9999349
## 2 -0.9922574 0.9925771 0.9918084 0.9885391 -0.9915297 -0.9999597
## 3 -0.9922574 0.9883902 0.9918084 0.9885391 -0.9882835 -0.9998942
## 4 -0.9897689 0.9883902 0.9925438 0.9932176 -0.9930045 -0.9999236
## 5 -0.9897689 0.9943032 0.9925438 0.9856091 -0.9939682 -0.9999692
## 6 -0.9926493 0.9943032 0.9933463 0.9856091 -0.9936092 -0.9999512
## attr98 attr99 attr100 attr101 attr102 attr103
## 1 -0.9998204 -0.9998785 -0.9944068 -0.9860249 -0.9886976 -0.8199493
## 2 -0.9996396 -0.9998454 -0.9939055 -0.9794351 -0.9928467 -0.8750964
## 3 -0.9996364 -0.9997950 -0.9878883 -0.9801445 -0.9813768 -0.7536287
## 4 -0.9998029 -0.9998829 -0.9947207 -0.9870330 -0.9883604 -0.8208042
## 5 -0.9998203 -0.9998599 -0.9959306 -0.9865242 -0.9900354 -0.8507439
## 6 -0.9998278 -0.9998560 -0.9953237 -0.9873590 -0.9890159 -0.7787178
## attr104 attr105 attr106 attr107 attr108 attr109
## 1 -0.7930464 -0.8631452 0.9480263 -0.334807052 0.7142020 0.4986861
## 2 -0.6553621 -0.7433264 0.4787576 -0.056439286 0.4697268 0.6490987
## 3 -0.6732736 -0.7233282 0.2723818 0.055575744 0.5605804 0.4815343
## 4 -0.7549682 -0.8004361 0.1415040 0.139563948 0.5542138 0.2895027
## 5 -0.7462578 -0.7725026 0.2500183 0.004544708 0.4110317 0.3904927
## 6 -0.7549682 -0.7665115 0.2865986 -0.028337038 0.3778878 0.2986920
## attr110 attr111 attr112 attr113 attr114 attr115
## 1 0.2966808 -0.18951272 0.3109116 0.2371101 0.4109366 -0.509475111
## 2 0.2140384 -0.08939874 0.3969624 0.2808034 0.2165530 0.112392130
## 3 0.1540988 -0.14811116 0.3621401 0.3070301 0.3366697 0.020750601
## 4 0.1718296 -0.23023560 0.2546607 0.3578172 0.4249952 -0.192279269
## 5 0.3663556 -0.26870767 0.4835351 0.2856164 0.4532194 -0.062401073
## 6 0.3947460 -0.21125744 0.5525029 0.2137284 0.4347620 -0.001329791
## attr116 attr117 attr118 attr119 attr120 attr121
## 1 0.4755736 -0.3522074 -0.3946309 -0.016790470 -0.15823668 -0.006100849
## 2 0.2554888 0.2017795 -0.2169136 0.032498466 -0.29512064 -0.016111620
## 3 0.3963886 0.2707450 -0.1276489 -0.157126194 -0.07482247 -0.031698294
## 4 0.5085598 0.4470294 -0.1350891 -0.130999590 0.40413819 -0.043409983
## 5 0.3724474 0.2134843 -0.2814568 0.051019425 0.02605744 -0.033960416
## 6 0.3563432 0.3157658 -0.3838693 -0.008798576 -0.14404291 -0.028775508
## attr122 attr123 attr124 attr125 attr126 attr127
## 1 0.007514728 -0.06386164 -0.9853121 -0.9766076 -0.9933188 -0.9845891
## 2 -0.027651251 -0.06848507 -0.9831218 -0.9890298 -0.9907206 -0.9868933
## 3 -0.039997164 -0.07137096 -0.9762939 -0.9935358 -0.9884102 -0.9749244
## 4 -0.032667105 -0.07822679 -0.9913866 -0.9923913 -0.9894005 -0.9915918
## 5 -0.021501776 -0.08350060 -0.9851854 -0.9923621 -0.9892721 -0.9869466
## 6 -0.018613112 -0.08245169 -0.9851826 -0.9921015 -0.9856284 -0.9857885
## attr128 attr129 attr130 attr131 attr132 attr133
## 1 -0.9763265 -0.9933414 -0.8975631 -0.9366760 -0.7626443 0.8542972
## 2 -0.9890117 -0.9906226 -0.8960751 -0.9564800 -0.7610341 0.8406589
## 3 -0.9940957 -0.9877144 -0.8960751 -0.9619768 -0.7585727 0.8406589
## 4 -0.9931157 -0.9909652 -0.9102716 -0.9595805 -0.7585727 0.8411034
## 5 -0.9925161 -0.9897482 -0.8997258 -0.9562789 -0.7647459 0.8460487
## 6 -0.9922423 -0.9850775 -0.8997258 -0.9562789 -0.7615367 0.8467689
## attr134 attr135 attr136 attr137 attr138 attr139
## 1 0.8950316 0.8308405 -0.9671216 -0.9995782 -0.9993543 -0.9998181
## 2 0.8883163 0.8289350 -0.9805500 -0.9997557 -0.9998973 -0.9998634
## 3 0.8859839 0.8289350 -0.9762173 -0.9996933 -0.9998283 -0.9998627
## 4 0.8859839 0.8266338 -0.9822325 -0.9997928 -0.9999023 -0.9999055
## 5 0.8913592 0.8213744 -0.9851988 -0.9998494 -0.9999519 -0.9998802
## 6 0.8913592 0.8188267 -0.9851510 -0.9998739 -0.9999466 -0.9998293
## attr140 attr141 attr142 attr143 attr144 attr145
## 1 -0.9843995 -0.9785768 -0.9930527 0.082631682 0.1745154 -0.2184370
## 2 -0.9932488 -0.9893073 -0.9903272 0.007469356 -0.5419790 -0.2266056
## 3 -0.9739585 -0.9951068 -0.9869179 -0.260942672 -1.0000000 -0.2932927
## 4 -0.9915519 -0.9941278 -0.9946692 -0.930551143 -0.8306202 -0.5707097
## 5 -0.9904046 -0.9932992 -0.9912416 -0.628860991 -0.4800923 -0.6717193
## 6 -0.9861885 -0.9929566 -0.9837923 -0.363801069 -0.3850386 -0.4942727
## attr146 attr147 attr148 attr149 attr150 attr151
## 1 0.32092613 -0.45260357 0.46613254 -0.20363231 1.00000000 -1.00000000
## 2 -0.06541049 -0.09176193 0.22188347 -0.12779766 -0.03572986 -0.08081796
## 3 -0.10490196 -0.04421066 0.16626233 -0.10284472 0.04275705 -0.14452158
## 4 0.11162856 -0.24433776 0.31459718 -0.15134107 0.05486659 -0.14180261
## 5 0.07426853 -0.23242548 0.37233310 -0.21590317 -0.15066477 0.17368060
## 6 -0.07750025 -0.04178307 0.09320668 0.03375017 -0.10760617 0.13739748
## attr152 attr153 attr154 attr155 attr156 attr157
## 1 0.3522760 0.4483984 0.75779313 -0.7824648 0.7037247 -0.39910653
## 2 0.1524217 0.1388310 0.09165939 -0.1920916 0.3364196 -0.22482272
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## 3 0.44007936 -0.4044275 -0.7618472 -0.11855926 0.177899475 0.1006992
## 4 0.43089077 -0.1383728 -0.4916043 -0.03678797 -0.012892494 0.6400110
## 5 0.13773462 -0.3662136 -0.7024898 0.12332005 0.122541962 0.6935783
## 6 0.07499891 -0.5549023 -0.8442241 0.08263216 -0.143439015 0.2750407
## attr558 attr559 attr560 attr561 targetVar
## 1 -0.01844588 -0.8415585 0.1799128 -0.05171842 5
## 2 0.70351059 -0.8450924 0.1802611 -0.04743634 5
## 3 0.80852908 -0.8492301 0.1806096 -0.04227136 5
## 4 -0.48536645 -0.8489466 0.1819071 -0.04082622 5
## 5 -0.61597061 -0.8481640 0.1851237 -0.03707990 5
## 6 -0.36822404 -0.8499269 0.1847950 -0.03532556 52.a.ii) Dimensions of the dataset.
dim(xy_train)## [1] 7767 5622.a.iii) Types of the attributes.
sapply(xy_train, class)## attr1 attr2 attr3 attr4 attr5 attr6 attr7
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric"
## attr8 attr9 attr10 attr11 attr12 attr13 attr14
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric"
## attr15 attr16 attr17 attr18 attr19 attr20 attr21
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric"
## attr22 attr23 attr24 attr25 attr26 attr27 attr28
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric"
## attr29 attr30 attr31 attr32 attr33 attr34 attr35
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric"
## attr36 attr37 attr38 attr39 attr40 attr41 attr42
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric"
## attr43 attr44 attr45 attr46 attr47 attr48 attr49
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric"
## attr50 attr51 attr52 attr53 attr54 attr55 attr56
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric"
## attr57 attr58 attr59 attr60 attr61 attr62 attr63
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric"
## attr64 attr65 attr66 attr67 attr68 attr69 attr70
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric"
## attr71 attr72 attr73 attr74 attr75 attr76 attr77
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric"
## attr78 attr79 attr80 attr81 attr82 attr83 attr84
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric"
## attr85 attr86 attr87 attr88 attr89 attr90 attr91
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric"
## attr92 attr93 attr94 attr95 attr96 attr97 attr98
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric"
## attr99 attr100 attr101 attr102 attr103 attr104 attr105
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric"
## attr106 attr107 attr108 attr109 attr110 attr111 attr112
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric"
## attr113 attr114 attr115 attr116 attr117 attr118 attr119
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric"
## attr120 attr121 attr122 attr123 attr124 attr125 attr126
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric"
## attr127 attr128 attr129 attr130 attr131 attr132 attr133
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric"
## attr134 attr135 attr136 attr137 attr138 attr139 attr140
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric"
## attr141 attr142 attr143 attr144 attr145 attr146 attr147
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric"
## attr148 attr149 attr150 attr151 attr152 attr153 attr154
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric"
## attr155 attr156 attr157 attr158 attr159 attr160 attr161
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric"
## attr162 attr163 attr164 attr165 attr166 attr167 attr168
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric"
## attr169 attr170 attr171 attr172 attr173 attr174 attr175
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric"
## attr176 attr177 attr178 attr179 attr180 attr181 attr182
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric"
## attr183 attr184 attr185 attr186 attr187 attr188 attr189
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric"
## attr190 attr191 attr192 attr193 attr194 attr195 attr196
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric"
## attr197 attr198 attr199 attr200 attr201 attr202 attr203
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric"
## attr204 attr205 attr206 attr207 attr208 attr209 attr210
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric"
## attr211 attr212 attr213 attr214 attr215 attr216 attr217
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric"
## attr218 attr219 attr220 attr221 attr222 attr223 attr224
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric"
## attr225 attr226 attr227 attr228 attr229 attr230 attr231
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric"
## attr232 attr233 attr234 attr235 attr236 attr237 attr238
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric"
## attr239 attr240 attr241 attr242 attr243 attr244 attr245
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric"
## attr246 attr247 attr248 attr249 attr250 attr251 attr252
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric"
## attr253 attr254 attr255 attr256 attr257 attr258 attr259
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric"
## attr260 attr261 attr262 attr263 attr264 attr265 attr266
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric"
## attr267 attr268 attr269 attr270 attr271 attr272 attr273
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric"
## attr274 attr275 attr276 attr277 attr278 attr279 attr280
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric"
## attr281 attr282 attr283 attr284 attr285 attr286 attr287
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric"
## attr288 attr289 attr290 attr291 attr292 attr293 attr294
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric"
## attr295 attr296 attr297 attr298 attr299 attr300 attr301
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric"
## attr302 attr303 attr304 attr305 attr306 attr307 attr308
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric"
## attr309 attr310 attr311 attr312 attr313 attr314 attr315
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric"
## attr316 attr317 attr318 attr319 attr320 attr321 attr322
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric"
## attr323 attr324 attr325 attr326 attr327 attr328 attr329
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric"
## attr330 attr331 attr332 attr333 attr334 attr335 attr336
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric"
## attr337 attr338 attr339 attr340 attr341 attr342 attr343
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric"
## attr344 attr345 attr346 attr347 attr348 attr349 attr350
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric"
## attr351 attr352 attr353 attr354 attr355 attr356 attr357
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric"
## attr358 attr359 attr360 attr361 attr362 attr363 attr364
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric"
## attr365 attr366 attr367 attr368 attr369 attr370 attr371
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric"
## attr372 attr373 attr374 attr375 attr376 attr377 attr378
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric"
## attr379 attr380 attr381 attr382 attr383 attr384 attr385
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric"
## attr386 attr387 attr388 attr389 attr390 attr391 attr392
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric"
## attr393 attr394 attr395 attr396 attr397 attr398 attr399
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric"
## attr400 attr401 attr402 attr403 attr404 attr405 attr406
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric"
## attr407 attr408 attr409 attr410 attr411 attr412 attr413
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric"
## attr414 attr415 attr416 attr417 attr418 attr419 attr420
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric"
## attr421 attr422 attr423 attr424 attr425 attr426 attr427
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric"
## attr428 attr429 attr430 attr431 attr432 attr433 attr434
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric"
## attr435 attr436 attr437 attr438 attr439 attr440 attr441
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric"
## attr442 attr443 attr444 attr445 attr446 attr447 attr448
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric"
## attr449 attr450 attr451 attr452 attr453 attr454 attr455
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric"
## attr456 attr457 attr458 attr459 attr460 attr461 attr462
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric"
## attr463 attr464 attr465 attr466 attr467 attr468 attr469
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric"
## attr470 attr471 attr472 attr473 attr474 attr475 attr476
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric"
## attr477 attr478 attr479 attr480 attr481 attr482 attr483
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric"
## attr484 attr485 attr486 attr487 attr488 attr489 attr490
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric"
## attr491 attr492 attr493 attr494 attr495 attr496 attr497
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric"
## attr498 attr499 attr500 attr501 attr502 attr503 attr504
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric"
## attr505 attr506 attr507 attr508 attr509 attr510 attr511
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric"
## attr512 attr513 attr514 attr515 attr516 attr517 attr518
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric"
## attr519 attr520 attr521 attr522 attr523 attr524 attr525
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric"
## attr526 attr527 attr528 attr529 attr530 attr531 attr532
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric"
## attr533 attr534 attr535 attr536 attr537 attr538 attr539
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric"
## attr540 attr541 attr542 attr543 attr544 attr545 attr546
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric"
## attr547 attr548 attr549 attr550 attr551 attr552 attr553
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric"
## attr554 attr555 attr556 attr557 attr558 attr559 attr560
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric"
## attr561 targetVar
## "numeric" "factor"2.a.iv) Statistical summary of all attributes.
summary(xy_train)## attr1 attr2 attr3
## Min. :-1.00000 Min. :-1.0000000 Min. :-1.00000
## 1st Qu.: 0.03204 1st Qu.:-0.0112093 1st Qu.:-0.02845
## Median : 0.03897 Median :-0.0029213 Median :-0.01960
## Mean : 0.03876 Mean :-0.0006466 Mean :-0.01815
## 3rd Qu.: 0.04400 3rd Qu.: 0.0043027 3rd Qu.:-0.01168
## Max. : 1.00000 Max. : 1.0000000 Max. : 1.00000
##
## attr4 attr5 attr6 attr7
## Min. :-1.0000 Min. :-1.0000 Min. :-1.0000 Min. :-1.0000
## 1st Qu.:-0.9921 1st Qu.:-0.9836 1st Qu.:-0.9847 1st Qu.:-0.9929
## Median :-0.9142 Median :-0.8280 Median :-0.8277 Median :-0.9244
## Mean :-0.5990 Mean :-0.6344 Mean :-0.6913 Mean :-0.6239
## 3rd Qu.:-0.2460 3rd Qu.:-0.3131 3rd Qu.:-0.4505 3rd Qu.:-0.2949
## Max. : 1.0000 Max. : 0.9460 Max. : 1.0000 Max. : 1.0000
##
## attr8 attr9 attr10 attr11
## Min. :-1.0000 Min. :-1.0000 Min. :-1.00000 Min. :-1.0000
## 1st Qu.:-0.9841 1st Qu.:-0.9867 1st Qu.:-0.79561 1st Qu.:-0.7407
## Median :-0.8386 Median :-0.8527 Median :-0.71701 Median :-0.6224
## Mean :-0.6579 Mean :-0.7402 Mean :-0.36020 Mean :-0.4925
## 3rd Qu.:-0.3627 3rd Qu.:-0.5405 3rd Qu.: 0.05418 3rd Qu.:-0.2847
## Max. : 0.9603 Max. : 1.0000 Max. : 1.00000 Max. : 1.0000
##
## attr12 attr13 attr14 attr15
## Min. :-1.0000 Min. :-1.0000 Min. :-1.0000 Min. :-1.0000
## 1st Qu.:-0.7068 1st Qu.: 0.2923 1st Qu.: 0.1205 1st Qu.: 0.2613
## Median :-0.6090 Median : 0.7707 Median : 0.6136 Median : 0.5885
## Mean :-0.4723 Mean : 0.5593 Mean : 0.4015 Mean : 0.4432
## 3rd Qu.:-0.2808 3rd Qu.: 0.8341 3rd Qu.: 0.7075 3rd Qu.: 0.6721
## Max. : 1.0000 Max. : 1.0000 Max. : 1.0000 Max. : 1.0000
##
## attr16 attr17 attr18 attr19
## Min. :-1.0000 Min. :-1.0000 Min. :-1.0000 Min. :-1.0000
## 1st Qu.:-0.9871 1st Qu.:-0.9999 1st Qu.:-0.9998 1st Qu.:-0.9998
## Median :-0.8547 Median :-0.9949 Median :-0.9851 Median :-0.9851
## Mean :-0.6491 Mean :-0.8258 Mean :-0.8950 Mean :-0.9264
## 3rd Qu.:-0.3457 3rd Qu.:-0.7263 3rd Qu.:-0.8375 3rd Qu.:-0.9006
## Max. : 1.0000 Max. : 1.0000 Max. : 0.9779 Max. : 1.0000
##
## attr20 attr21 attr22 attr23
## Min. :-1.0000 Min. :-1.0000 Min. :-1.0000 Min. :-1.00000
## 1st Qu.:-0.9938 1st Qu.:-0.9873 1st Qu.:-0.9886 1st Qu.:-0.67065
## Median :-0.9328 Median :-0.8839 Median :-0.8864 Median :-0.28099
## Mean :-0.6770 Mean :-0.7372 Mean :-0.7940 Mean :-0.29896
## 3rd Qu.:-0.3909 3rd Qu.:-0.5248 3rd Qu.:-0.6426 3rd Qu.: 0.02878
## Max. : 1.0000 Max. : 1.0000 Max. : 1.0000 Max. : 1.00000
##
## attr24 attr25 attr26 attr27
## Min. :-1.0000 Min. :-1.0000 Min. :-1.0000 Min. :-1.00000
## 1st Qu.:-0.5863 1st Qu.:-0.5299 1st Qu.:-0.3692 1st Qu.:-0.04681
## Median :-0.1567 Median :-0.1781 Median :-0.1481 Median : 0.08796
## Mean :-0.1815 Mean :-0.1953 Mean :-0.1255 Mean : 0.11461
## 3rd Qu.: 0.1993 3rd Qu.: 0.1124 3rd Qu.: 0.1228 3rd Qu.: 0.26730
## Max. : 1.0000 Max. : 0.9998 Max. : 1.0000 Max. : 1.00000
##
## attr28 attr29 attr30
## Min. :-1.000000 Min. :-0.93037 Min. :-1.00000
## 1st Qu.:-0.152010 1st Qu.:-0.12769 1st Qu.:-0.20740
## Median : 0.003232 Median : 0.04035 Median :-0.03653
## Mean :-0.013326 Mean : 0.03539 Mean :-0.01856
## 3rd Qu.: 0.136935 3rd Qu.: 0.19850 3rd Qu.: 0.17333
## Max. : 1.000000 Max. : 1.00000 Max. : 1.00000
##
## attr31 attr32 attr33
## Min. :-1.00000 Min. :-1.00000 Min. :-0.90971
## 1st Qu.:-0.18465 1st Qu.: 0.06698 1st Qu.:-0.09028
## Median :-0.04382 Median : 0.18080 Median : 0.04813
## Mean :-0.03071 Mean : 0.17369 Mean : 0.04787
## 3rd Qu.: 0.11213 3rd Qu.: 0.28884 3rd Qu.: 0.18709
## Max. : 1.00000 Max. : 1.00000 Max. : 0.99290
##
## attr34 attr35 attr36
## Min. :-1.00000 Min. :-0.97693 Min. :-1.00000
## 1st Qu.:-0.05212 1st Qu.:-0.17760 1st Qu.:-0.03675
## Median : 0.15061 Median :-0.05570 Median : 0.10904
## Mean : 0.13832 Mean :-0.03068 Mean : 0.09661
## 3rd Qu.: 0.33184 3rd Qu.: 0.10365 3rd Qu.: 0.24399
## Max. : 0.91541 Max. : 1.00000 Max. : 0.96924
##
## attr37 attr38 attr39
## Min. :-1.00000 Min. :-1.00000 Min. :-1.000000
## 1st Qu.:-0.24979 1st Qu.:-0.38748 1st Qu.:-0.412106
## Median :-0.08732 Median :-0.16776 Median :-0.192983
## Mean :-0.08308 Mean :-0.13143 Mean :-0.195810
## 3rd Qu.: 0.07848 3rd Qu.: 0.07219 3rd Qu.: 0.007006
## Max. : 0.88413 Max. : 1.00000 Max. : 1.000000
##
## attr40 attr41 attr42 attr43
## Min. :-0.9825 Min. :-1.0000 Min. :-0.53822 Min. :-1.00000
## 1st Qu.:-0.1564 1st Qu.: 0.7761 1st Qu.:-0.23172 1st Qu.:-0.11782
## Median : 0.1480 Median : 0.9126 Median :-0.13117 Median : 0.03384
## Mean : 0.1064 Mean : 0.6552 Mean : 0.02554 Mean : 0.09809
## 3rd Qu.: 0.3892 3rd Qu.: 0.9484 3rd Qu.: 0.19152 3rd Qu.: 0.23909
## Max. : 1.0000 Max. : 0.9847 Max. : 1.00000 Max. : 1.00000
##
## attr44 attr45 attr46 attr47
## Min. :-1.0000 Min. :-0.9999 Min. :-1.0000 Min. :-1.0000
## 1st Qu.:-0.9956 1st Qu.:-0.9914 1st Qu.:-0.9908 1st Qu.:-0.9958
## Median :-0.9841 Median :-0.9753 Median :-0.9758 Median :-0.9853
## Mean :-0.9436 Mean :-0.9261 Mean :-0.9368 Mean :-0.9467
## 3rd Qu.:-0.9641 3rd Qu.:-0.9433 3rd Qu.:-0.9456 3rd Qu.:-0.9663
## Max. : 1.0000 Max. : 1.0000 Max. : 1.0000 Max. : 1.0000
##
## attr48 attr49 attr50 attr51
## Min. :-1.0000 Min. :-1.0000 Min. :-1.0000 Min. :-0.49393
## 1st Qu.:-0.9917 1st Qu.:-0.9911 1st Qu.: 0.7432 1st Qu.:-0.24294
## Median :-0.9767 Median :-0.9770 Median : 0.8569 Median :-0.14457
## Mean :-0.9288 Mean :-0.9389 Mean : 0.6111 Mean : 0.01543
## 3rd Qu.:-0.9458 3rd Qu.:-0.9478 3rd Qu.: 0.8867 3rd Qu.: 0.19408
## Max. : 1.0000 Max. : 1.0000 Max. : 1.0000 Max. : 0.96811
##
## attr52 attr53 attr54
## Min. :-1.00000 Min. :-1.0000 Min. :-0.64863
## 1st Qu.:-0.11005 1st Qu.: 0.7680 1st Qu.:-0.22357
## Median : 0.04789 Median : 0.9236 Median :-0.12500
## Mean : 0.11048 Mean : 0.6613 Mean : 0.02503
## 3rd Qu.: 0.25594 3rd Qu.: 0.9628 3rd Qu.: 0.16822
## Max. : 0.99659 Max. : 1.0000 Max. : 1.00000
##
## attr55 attr56 attr57 attr58
## Min. :-1.00000 Min. :-1.00000 Min. :-1.0000 Min. :-1.0000
## 1st Qu.:-0.14525 1st Qu.:-0.39233 1st Qu.: 0.4390 1st Qu.:-0.9654
## Median : 0.01094 Median :-0.10281 Median : 0.7693 Median :-0.9073
## Mean : 0.07602 Mean :-0.07242 Mean : 0.4182 Mean :-0.7216
## 3rd Qu.: 0.21594 3rd Qu.: 0.23295 3rd Qu.: 0.8615 3rd Qu.:-0.7560
## Max. : 1.00000 Max. : 1.00000 Max. : 0.9591 Max. : 1.0000
##
## attr59 attr60 attr61 attr62
## Min. :-1.0000 Min. :-1.0000 Min. :-1.0000 Min. :-1.0000
## 1st Qu.:-0.9892 1st Qu.:-0.9964 1st Qu.:-0.9931 1st Qu.:-0.9924
## Median :-0.9401 Median :-0.9883 Median :-0.9813 Median :-0.9806
## Mean :-0.7438 Mean :-0.9560 Mean :-0.9393 Mean :-0.9460
## 3rd Qu.:-0.7337 3rd Qu.:-0.9722 3rd Qu.:-0.9548 3rd Qu.:-0.9548
## Max. : 1.0000 Max. : 1.0000 Max. : 0.9348 Max. : 1.0000
##
## attr63 attr64 attr65 attr66
## Min. :-1.0000 Min. :-1.0000 Min. :-1.0000 Min. :-1.0000
## 1st Qu.:-1.0000 1st Qu.:-1.0000 1st Qu.:-1.0000 1st Qu.:-0.6799
## Median :-0.7357 Median :-1.0000 Median :-0.8269 Median :-0.5386
## Mean :-0.6471 Mean :-0.8232 Mean :-0.6684 Mean :-0.5355
## 3rd Qu.:-0.3915 3rd Qu.:-0.7794 3rd Qu.:-0.4215 3rd Qu.:-0.3900
## Max. : 1.0000 Max. : 1.0000 Max. : 1.0000 Max. : 1.0000
##
## attr67 attr68 attr69 attr70
## Min. :-1.0000 Min. :-1.0000 Min. :-1.0000 Min. :-1.0000
## 1st Qu.: 0.4285 1st Qu.:-0.7645 1st Qu.: 0.4967 1st Qu.:-0.5266
## Median : 0.5824 Median :-0.6286 Median : 0.6714 Median :-0.2788
## Mean : 0.5719 Mean :-0.6078 Mean : 0.6432 Mean :-0.2869
## 3rd Qu.: 0.7219 3rd Qu.:-0.4640 3rd Qu.: 0.8079 3rd Qu.:-0.0497
## Max. : 1.0000 Max. : 1.0000 Max. : 1.0000 Max. : 1.0000
##
## attr71 attr72 attr73 attr74
## Min. :-1.0000 Min. :-1.0000 Min. :-1.0000 Min. :-1.0000
## 1st Qu.: 0.1060 1st Qu.:-0.5845 1st Qu.: 0.2233 1st Qu.:-0.6586
## Median : 0.3211 Median :-0.3723 Median : 0.4275 Median :-0.4553
## Mean : 0.3293 Mean :-0.3729 Mean : 0.4164 Mean :-0.4589
## 3rd Qu.: 0.5519 3rd Qu.:-0.1700 3rd Qu.: 0.6245 3rd Qu.:-0.2660
## Max. : 1.0000 Max. : 1.0000 Max. : 0.9996 Max. : 0.6314
##
## attr75 attr76 attr77 attr78
## Min. :-0.6001 Min. :-1.0000 Min. :-0.5353 Min. :-1.0000
## 1st Qu.: 0.2956 1st Qu.:-0.6996 1st Qu.: 0.3486 1st Qu.:-0.5585
## Median : 0.4794 Median :-0.5032 Median : 0.5310 Median : 0.3588
## Mean : 0.4828 Mean :-0.5064 Mean : 0.5287 Mean : 0.1573
## 3rd Qu.: 0.6788 3rd Qu.:-0.3234 3rd Qu.: 0.7218 3rd Qu.: 0.8385
## Max. : 1.0000 Max. : 0.5679 Max. : 1.0000 Max. : 1.0000
##
## attr79 attr80 attr81
## Min. :-1.0000 Min. :-1.0000 Min. :-1.00000
## 1st Qu.:-0.8244 1st Qu.:-0.5955 1st Qu.: 0.05899
## Median :-0.2402 Median : 0.2198 Median : 0.07592
## Mean :-0.1133 Mean : 0.1043 Mean : 0.07747
## 3rd Qu.: 0.6091 3rd Qu.: 0.8064 3rd Qu.: 0.09542
## Max. : 1.0000 Max. : 1.0000 Max. : 1.00000
##
## attr82 attr83 attr84
## Min. :-1.000000 Min. :-0.91882 Min. :-1.0000
## 1st Qu.:-0.022742 1st Qu.:-0.06928 1st Qu.:-0.9913
## Median : 0.010691 Median :-0.03903 Median :-0.9379
## Mean : 0.006721 Mean :-0.04034 Mean :-0.6495
## 3rd Qu.: 0.036395 3rd Qu.:-0.01158 3rd Qu.:-0.3087
## Max. : 1.000000 Max. : 0.91283 Max. : 1.0000
##
## attr85 attr86 attr87 attr88
## Min. :-1.0000 Min. :-1.0000 Min. :-1.0000 Min. :-1.0000
## 1st Qu.:-0.9854 1st Qu.:-0.9892 1st Qu.:-0.9913 1st Qu.:-0.9837
## Median :-0.9031 Median :-0.9394 Median :-0.9459 Median :-0.9084
## Mean :-0.6120 Mean :-0.7619 Mean :-0.6467 Mean :-0.5970
## 3rd Qu.:-0.2388 3rd Qu.:-0.5587 3rd Qu.:-0.2987 3rd Qu.:-0.2009
## Max. : 0.8071 Max. : 1.0000 Max. : 1.0000 Max. : 1.0000
##
## attr89 attr90 attr91 attr92
## Min. :-1.0000 Min. :-1.0000 Min. :-1.0000 Min. :-1.0000
## 1st Qu.:-0.9879 1st Qu.:-0.9918 1st Qu.:-0.9902 1st Qu.:-0.9897
## Median :-0.9421 Median :-0.9263 Median :-0.9231 Median :-0.9409
## Mean :-0.7559 Mean :-0.7032 Mean :-0.7503 Mean :-0.8184
## 3rd Qu.:-0.5467 3rd Qu.:-0.4770 3rd Qu.:-0.5403 3rd Qu.:-0.6886
## Max. : 1.0000 Max. : 1.0000 Max. : 0.6244 Max. : 1.0000
##
## attr93 attr94 attr95 attr96
## Min. :-1.0000 Min. :-0.7469 Min. :-1.0000 Min. :-1.0000
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## Median : 0.9187 Median : 0.9105 Median : 0.9225 Median :-0.9329
## Mean : 0.6285 Mean : 0.6889 Mean : 0.7382 Mean :-0.6519
## 3rd Qu.: 0.9897 3rd Qu.: 0.9888 3rd Qu.: 0.9866 3rd Qu.:-0.2986
## Max. : 1.0000 Max. : 1.0000 Max. : 0.9993 Max. : 1.0000
##
## attr97 attr98 attr99 attr100
## Min. :-1.0000 Min. :-1.0000 Min. :-1.0000 Min. :-1.0000
## 1st Qu.:-0.9999 1st Qu.:-0.9998 1st Qu.:-0.9998 1st Qu.:-0.9900
## Median :-0.9977 Median :-0.9944 Median :-0.9973 Median :-0.9530
## Mean :-0.8563 Mean :-0.8327 Mean :-0.9296 Mean :-0.6366
## 3rd Qu.:-0.7583 3rd Qu.:-0.7057 3rd Qu.:-0.8975 3rd Qu.:-0.2845
## Max. : 1.0000 Max. : 0.6344 Max. : 1.0000 Max. : 1.0000
##
## attr101 attr102 attr103 attr104
## Min. :-1.0000 Min. :-1.0000 Min. :-1.00000 Min. :-1.00000
## 1st Qu.:-0.9839 1st Qu.:-0.9858 1st Qu.:-0.73089 1st Qu.:-0.72998
## Median :-0.9325 Median :-0.9476 Median :-0.25949 Median :-0.21553
## Mean :-0.6596 Mean :-0.7699 Mean :-0.08536 Mean :-0.08115
## 3rd Qu.:-0.3325 3rd Qu.:-0.5874 3rd Qu.: 0.57841 3rd Qu.: 0.56261
## Max. : 1.0000 Max. : 1.0000 Max. : 1.00000 Max. : 1.00000
##
## attr105 attr106 attr107
## Min. :-1.0000 Min. :-1.00000 Min. :-1.00000
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## Median :-0.2925 Median :-0.08559 Median : 0.03561
## Mean :-0.1039 Mean :-0.07669 Mean : 0.03416
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## Max. : 1.0000 Max. : 1.00000 Max. : 1.00000
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## attr108 attr109 attr110
## Min. :-1.00000 Min. :-1.00000 Min. :-1.000000
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## Median : 0.20835 Median : 0.21036 Median :-0.004985
## Mean : 0.19884 Mean : 0.20278 Mean : 0.008669
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## Max. : 0.94451 Max. : 1.00000 Max. : 1.000000
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## attr111 attr112 attr113
## Min. :-0.96851 Min. :-1.0000 Min. :-1.00000
## 1st Qu.:-0.20318 1st Qu.: 0.1045 1st Qu.: 0.02307
## Median :-0.08796 Median : 0.2424 Median : 0.17725
## Mean :-0.08602 Mean : 0.2334 Mean : 0.16785
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## attr114 attr115 attr116
## Min. :-1.00000 Min. :-1.00000 Min. :-0.87812
## 1st Qu.:-0.11162 1st Qu.:-0.07507 1st Qu.: 0.04303
## Median : 0.08606 Median : 0.03030 Median : 0.21046
## Mean : 0.07209 Mean : 0.03025 Mean : 0.19363
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## attr117 attr118 attr119
## Min. :-1.0000 Min. :-1.00000 Min. :-1.00000
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## Median : 0.1799 Median :-0.15334 Median :-0.03919
## Mean : 0.1661 Mean :-0.15177 Mean :-0.04239
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## attr120 attr121 attr122
## Min. :-0.93231 Min. :-0.914050 Min. :-1.000000
## 1st Qu.:-0.13298 1st Qu.:-0.047501 1st Qu.:-0.043021
## Median : 0.03930 Median :-0.027678 Median :-0.021450
## Mean : 0.04614 Mean :-0.028705 Mean :-0.020532
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## Max. : 0.92736 Max. : 0.740403 Max. : 0.742382
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## attr123 attr124 attr125 attr126
## Min. :-0.97271 Min. :-1.0000 Min. :-1.0000 Min. :-0.9999
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## Median :-0.07785 Median :-0.8608 Median :-0.8798 Median :-0.8666
## Mean :-0.07750 Mean :-0.7083 Mean :-0.6643 Mean :-0.6888
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## Max. : 0.92052 Max. : 1.0000 Max. : 1.0000 Max. : 0.6850
##
## attr127 attr128 attr129 attr130
## Min. :-1.0000 Min. :-1.0000 Min. :-0.9998 Min. :-1.0000
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## Median :-0.8711 Median :-0.8925 Median :-0.8694 Median :-0.8325
## Mean :-0.7147 Mean :-0.6770 Mean :-0.6945 Mean :-0.7345
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##
## attr131 attr132 attr133 attr134
## Min. :-1.0000 Min. :-0.9514 Min. :-1.0000 Min. :-1.0000
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## Median :-0.8688 Median :-0.6316 Median : 0.7605 Median : 0.8120
## Mean :-0.7302 Mean :-0.5001 Mean : 0.6325 Mean : 0.7091
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## Max. : 1.0000 Max. : 0.9216 Max. : 1.0000 Max. : 1.0000
##
## attr135 attr136 attr137 attr138
## Min. :-1.0000 Min. :-1.0000 Min. :-1.0000 Min. :-1.0000
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## Median : 0.7155 Median :-0.7503 Median :-0.9806 Median :-0.9858
## Mean : 0.5481 Mean :-0.5784 Mean :-0.8948 Mean :-0.8725
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## Max. : 1.0000 Max. : 1.0000 Max. : 1.0000 Max. : 1.0000
##
## attr139 attr140 attr141 attr142
## Min. :-1.0000 Min. :-1.0000 Min. :-1.0000 Min. :-0.9999
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## Median :-0.9713 Median :-0.9007 Median :-0.9132 Median :-0.8731
## Mean :-0.8857 Mean :-0.7361 Mean :-0.7024 Mean :-0.6972
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##
## attr143 attr144 attr145
## Min. :-1.0000 Min. :-1.00000 Min. :-1.00000
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## Median :-0.1698 Median :-0.08972 Median :-0.03049
## Mean :-0.1381 Mean :-0.11729 Mean :-0.11798
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## Max. : 1.0000 Max. : 1.00000 Max. : 1.00000
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## attr146 attr147 attr148
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## Median : 0.04031 Median :-0.11941 Median : 0.16537
## Mean : 0.05686 Mean :-0.11252 Mean : 0.14971
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## attr149 attr150 attr151
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## Median :-0.06412 Median :-0.20481 Median : 0.15360
## Mean :-0.06574 Mean :-0.20113 Mean : 0.15940
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##
## attr152 attr153 attr154
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## Median :-0.005872 Median : 0.20463 Median :-0.07768
## Mean :-0.011001 Mean : 0.20392 Mean :-0.04654
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## attr155 attr156 attr157
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## Median : 0.03106 Median : 0.06815 Median : 0.06692
## Mean : 0.02233 Mean : 0.05014 Mean : 0.06697
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## attr158 attr159 attr160
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## Median :-0.1819 Median :-0.0201672 Median :-0.1153
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## Max. : 1.0000 Max. : 1.0000000 Max. : 1.0000
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## attr161 attr162 attr163
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## Median :-0.09822 Median :-0.04053 Median :-0.05455
## Mean :-0.09782 Mean :-0.04182 Mean :-0.05446
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## attr164 attr165 attr166 attr167
## Min. :-1.0000 Min. :-1.0000 Min. :-1.0000 Min. :-1.0000
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## Median :-0.9121 Median :-0.9416 Median :-0.9339 Median :-0.9243
## Mean :-0.7303 Mean :-0.7855 Mean :-0.7440 Mean :-0.7288
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## Max. : 1.0000 Max. : 1.0000 Max. : 1.0000 Max. : 1.0000
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## attr168 attr169 attr170 attr171
## Min. :-1.0000 Min. :-1.0000 Min. :-1.0000 Min. :-1.0000
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## Median :-0.9513 Median :-0.9440 Median :-0.9187 Median :-0.9380
## Mean :-0.7961 Mean :-0.7504 Mean :-0.7925 Mean :-0.8090
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## Max. : 1.0000 Max. : 1.0000 Max. : 0.5985 Max. : 1.0000
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## attr172 attr173 attr174 attr175
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## Median :-0.9173 Median : 0.9058 Median : 0.9450 Median : 0.9399
## Mean :-0.7473 Mean : 0.7587 Mean : 0.8312 Mean : 0.8017
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##
## attr176 attr177 attr178 attr179
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## Median :-0.9439 Median :-0.9958 Median :-0.9981 Median :-0.9974
## Mean :-0.7672 Mean :-0.9164 Mean :-0.9385 Mean :-0.9219
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## attr180 attr181 attr182 attr183
## Min. :-1.0000 Min. :-1.0000 Min. :-1.0000 Min. :-1.000000
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## Median :-0.9420 Median :-0.9633 Median :-0.9597 Median : 0.040187
## Mean :-0.7363 Mean :-0.8081 Mean :-0.7695 Mean :-0.007699
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## attr184 attr185 attr186
## Min. :-1.000000 Min. :-1.000000 Min. :-1.00000
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## Median : 0.058444 Median :-0.056546 Median : 0.02851
## Mean : 0.008778 Mean :-0.009301 Mean : 0.04283
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## attr187 attr188 attr189
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## Median : 0.08167 Median : 0.07566 Median : 0.145095
## Mean : 0.08427 Mean : 0.06696 Mean : 0.136062
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## attr190 attr191 attr192
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## Median :-0.144269 Median : 0.11353 Median : 0.07793
## Mean :-0.138584 Mean : 0.11311 Mean : 0.06814
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##
## attr193 attr194 attr195
## Min. :-1.00000 Min. :-1.000000 Min. :-1.00000
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## Median : 0.10914 Median :-0.005731 Median :-0.12313
## Mean : 0.10624 Mean : 0.038275 Mean :-0.11361
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## attr196 attr197 attr198
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## Median : 0.25224 Median : 0.148567 Median : 0.02007
## Mean : 0.24347 Mean : 0.138984 Mean : 0.02301
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##
## attr199 attr200 attr201 attr202
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## Median : 0.03762 Median :-0.10468 Median :-0.8451 Median :-0.7945
## Mean : 0.04121 Mean :-0.10331 Mean :-0.6276 Mean :-0.6547
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##
## attr203 attr204 attr205 attr206
## Min. :-1.0000 Min. :-1.0000 Min. :-1.0000 Min. :-1.0000
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## Median :-0.8084 Median :-0.7484 Median :-0.9658 Median :-0.8451
## Mean :-0.6937 Mean :-0.5322 Mean :-0.8647 Mean :-0.6276
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## Max. : 0.9080 Max. : 1.0000 Max. : 1.0000 Max. : 1.0000
##
## attr207 attr208 attr209 attr210
## Min. :-1.0000 Min. :-1.0000 Min. :-1.0000 Min. :-1.00000
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## Median :-0.9826 Median :-0.8505 Median : 0.3319 Median :-0.04842
## Mean :-0.8511 Mean :-0.7584 Mean : 0.1669 Mean :-0.04536
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## Max. : 1.0000 Max. : 0.9616 Max. : 1.0000 Max. : 1.00000
##
## attr211 attr212 attr213
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## Mean : 0.0101903 Mean : 0.12498 Mean :-0.03631
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##
## attr214 attr215 attr216 attr217
## Min. :-1.0000 Min. :-1.0000 Min. :-1.0000 Min. :-1.0000
## 1st Qu.:-0.9863 1st Qu.:-0.9854 1st Qu.:-0.9872 1st Qu.:-0.9809
## Median :-0.8451 Median :-0.7945 Median :-0.8084 Median :-0.7484
## Mean :-0.6276 Mean :-0.6547 Mean :-0.6937 Mean :-0.5322
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## attr218 attr219 attr220 attr221
## Min. :-1.0000 Min. :-1.0000 Min. :-1.0000 Min. :-1.0000
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## Median :-0.9658 Median :-0.8451 Median :-0.9826 Median :-0.8505
## Mean :-0.8647 Mean :-0.6276 Mean :-0.8511 Mean :-0.7584
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## Median : 0.3319 Median :-0.04842 Median :-0.0000395
## Mean : 0.1669 Mean :-0.04536 Mean : 0.0101903
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## Max. : 1.0000 Max. : 1.00000 Max. : 1.0000000
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## attr225 attr226 attr227 attr228
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## Median : 0.13905 Median :-0.03845 Median :-0.9346 Median :-0.9056
## Mean : 0.12498 Mean :-0.03631 Mean :-0.6551 Mean :-0.6356
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## Median :-0.9182 Median :-0.8997 Median :-0.9578 Median :-0.9346
## Mean :-0.6549 Mean :-0.6440 Mean :-0.7893 Mean :-0.6551
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## Min. :-1.0000 Min. :-1.0000 Min. :-1.00000 Min. :-1.00000
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## Median :-0.9961 Median :-0.9407 Median :-0.21849 Median : 0.11206
## Mean :-0.8551 Mean :-0.7058 Mean :-0.05457 Mean : 0.10032
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## attr237 attr238 attr239
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## Median :-0.06959 Median :-0.18429 Median : 0.05664
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## Median :-0.7463 Median :-0.7735 Median :-0.7642 Median :-0.8014
## Mean :-0.5815 Mean :-0.6363 Mean :-0.6233 Mean :-0.6805
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## Median :-0.9164 Median :-0.7463 Median :-0.9637 Median :-0.7897
## Mean :-0.8339 Mean :-0.5815 Mean :-0.8184 Mean :-0.6661
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## attr248 attr249 attr250
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## Median : 0.37452 Median :-0.009819 Median :-0.19876
## Mean : 0.32016 Mean :-0.006519 Mean :-0.18354
## 3rd Qu.: 0.69117 3rd Qu.: 0.190419 3rd Qu.:-0.01234
## Max. : 1.00000 Max. : 1.000000 Max. : 0.93765
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## attr251 attr252 attr253 attr254
## Min. :-1.00000 Min. :-0.84977 Min. :-1.0000 Min. :-1.0000
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## Median : 0.20104 Median :-0.03058 Median :-0.9419 Median :-0.9205
## Mean : 0.19650 Mean :-0.02703 Mean :-0.7622 Mean :-0.7782
## 3rd Qu.: 0.35395 3rd Qu.: 0.13740 3rd Qu.:-0.5555 3rd Qu.:-0.6156
## Max. : 1.00000 Max. : 1.00000 Max. : 1.0000 Max. : 1.0000
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## attr255 attr256 attr257 attr258
## Min. :-1.0000 Min. :-1.0000 Min. :-1.0000 Min. :-1.0000
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## Median :-0.9311 Median :-0.9218 Median :-0.9662 Median :-0.9419
## Mean :-0.7927 Mean :-0.7849 Mean :-0.8054 Mean :-0.7622
## 3rd Qu.:-0.6349 3rd Qu.:-0.6403 3rd Qu.:-0.6518 3rd Qu.:-0.5555
## Max. : 1.0000 Max. : 1.0000 Max. : 1.0000 Max. : 1.0000
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## attr259 attr260 attr261 attr262
## Min. :-1.0000 Min. :-1.0000 Min. :-1.0000 Min. :-1.0000
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## Median :-0.9975 Median :-0.9430 Median : 0.1848 Median : 0.3243
## Mean :-0.9314 Mean :-0.8060 Mean : 0.1364 Mean : 0.3073
## 3rd Qu.:-0.9045 3rd Qu.:-0.6506 3rd Qu.: 0.8385 3rd Qu.: 0.4718
## Max. : 1.0000 Max. : 1.0000 Max. : 1.0000 Max. : 1.0000
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## attr263 attr264 attr265 attr266
## Min. :-1.0000 Min. :-1.00000 Min. :-1.00000 Min. :-1.0000
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## Median :-0.1965 Median :-0.11409 Median :-0.04524 Median :-0.9163
## Mean :-0.1871 Mean :-0.11597 Mean :-0.03288 Mean :-0.6211
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## attr267 attr268 attr269 attr270
## Min. :-1.00000 Min. :-1.0000 Min. :-1.0000 Min. :-1.0000
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## Median :-0.80189 Median :-0.8357 Median :-0.9157 Median :-0.8441
## Mean :-0.52151 Mean :-0.6477 Mean :-0.5921 Mean :-0.6838
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## attr271 attr272 attr273 attr274
## Min. :-1.0000 Min. :-1.0000 Min. :-1.00000 Min. :-1.0000
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## Median :-0.8368 Median :-0.9141 Median :-0.79130 Median :-0.8079
## Mean :-0.7284 Mean :-0.5878 Mean :-0.50683 Mean :-0.6099
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## attr275 attr276 attr277 attr278
## Min. :-1.0000 Min. :-1.0000 Min. :-1.0000 Min. :-1.0000
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## Median :-0.9161 Median :-0.8653 Median :-0.8612 Median :-0.9715
## Mean :-0.6375 Mean :-0.7697 Mean :-0.7894 Mean :-0.8479
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## attr279 attr280 attr281 attr282
## Min. :-1.0000 Min. :-1.0000 Min. :-1.0000 Min. :-1.0000
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## Median :-0.9645 Median :-0.9705 Median :-0.8291 Median :-0.9960
## Mean :-0.8685 Mean :-0.9041 Mean :-0.5435 Mean :-0.8212
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## attr283 attr284 attr285 attr286
## Min. :-1.0000 Min. :-1.0000 Min. :-1.0000 Min. :-1.0000
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## Median :-0.9841 Median :-0.9833 Median :-0.9262 Median :-0.8989
## Mean :-0.8640 Mean :-0.8981 Mean :-0.6591 Mean :-0.6517
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## attr287 attr288 attr289 attr290
## Min. :-1.0000 Min. :-1.0000 Min. :-1.0000 Min. :-1.0000
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## Median :-0.9182 Median :-0.3658 Median :-0.2403 Median :-0.2411
## Mean :-0.7489 Mean :-0.1920 Mean :-0.1717 Mean :-0.1913
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## attr291 attr292 attr293 attr294
## Min. :-1.0000 Min. :-1.0000 Min. :-1.0000 Min. :-1.00000
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## Median :-0.8000 Median :-0.8667 Median :-0.9231 Median :-0.13670
## Mean :-0.7696 Mean :-0.8059 Mean :-0.8541 Mean :-0.11748
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## attr295 attr296 attr297 attr298
## Min. :-0.93407 Min. :-1.00000 Min. :-0.8760 Min. :-1.0000
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## Median : 0.02356 Median : 0.13610 Median :-0.1491 Median :-0.5614
## Mean : 0.02994 Mean : 0.12067 Mean :-0.1103 Mean :-0.4379
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## attr299 attr300 attr301 attr302
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## Median :-0.38032 Median :-0.6942 Median :-0.26036 Median :-0.5827
## Mean :-0.27032 Mean :-0.5340 Mean :-0.18701 Mean :-0.4528
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## attr303 attr304 attr305 attr306
## Min. :-1.0000 Min. :-1.0000 Min. :-1.0000 Min. :-1.0000
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## Median :-0.9960 Median :-0.9982 Median :-0.9969 Median :-0.9965
## Mean :-0.8089 Mean :-0.8926 Mean :-0.8637 Mean :-0.8990
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## attr307 attr308 attr309 attr310
## Min. :-1.0000 Min. :-1.0000 Min. :-1.0000 Min. :-1.0000
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## Median :-0.9969 Median :-0.9972 Median :-0.9980 Median :-0.9995
## Mean :-0.9157 Mean :-0.9129 Mean :-0.9451 Mean :-0.9527
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## attr311 attr312 attr313 attr314
## Min. :-1.0000 Min. :-1.0000 Min. :-1.0000 Min. :-1.0000
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## Median :-0.9962 Median :-0.9962 Median :-0.9972 Median :-0.9981
## Mean :-0.8158 Mean :-0.8529 Mean :-0.9147 Mean :-0.9477
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## Max. : 1.0000 Max. : 1.0000 Max. : 1.0000 Max. : 1.0000
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## attr315 attr316 attr317 attr318
## Min. :-1.0000 Min. :-1.0000 Min. :-1.0000 Min. :-1.0000
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## Median :-0.9961 Median :-0.9961 Median :-0.9866 Median :-0.9936
## Mean :-0.8192 Mean :-0.8869 Mean :-0.9113 Mean :-0.8496
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## attr319 attr320 attr321 attr322
## Min. :-1.0000 Min. :-1.0000 Min. :-1.0000 Min. :-1.0000
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## Median :-0.9952 Median :-0.9946 Median :-0.9915 Median :-0.9897
## Mean :-0.8652 Mean :-0.9063 Mean :-0.8966 Mean :-0.8798
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## attr323 attr324 attr325 attr326
## Min. :-1.0000 Min. :-1.0000 Min. :-1.0000 Min. :-1.0000
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## Median :-0.9895 Median :-0.9985 Median :-0.9850 Median :-0.9938
## Mean :-0.8964 Mean :-0.9424 Mean :-0.8783 Mean :-0.8427
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## attr327 attr328 attr329 attr330
## Min. :-1.0000 Min. :-1.0000 Min. :-1.0000 Min. :-1.0000
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## Median :-0.9895 Median :-0.9901 Median :-0.9844 Median :-0.9929
## Mean :-0.8783 Mean :-0.9125 Mean :-0.8677 Mean :-0.8928
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## attr331 attr332 attr333 attr334
## Min. :-1.0000 Min. :-1.0000 Min. :-1.0000 Min. :-1.0000
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## Median :-0.9845 Median :-0.9937 Median :-0.9968 Median :-0.9977
## Mean :-0.9255 Mean :-0.8978 Mean :-0.9243 Mean :-0.9605
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## Max. : 1.0000 Max. : 1.0000 Max. : 1.0000 Max. : 1.0000
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## attr335 attr336 attr337 attr338
## Min. :-1.0000 Min. :-1.0000 Min. :-1.0000 Min. :-1.0000
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## Median :-0.9968 Median :-0.9928 Median :-0.9918 Median :-0.9982
## Mean :-0.9617 Mean :-0.9334 Mean :-0.9365 Mean :-0.9516
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## attr339 attr340 attr341 attr342
## Min. :-1.0000 Min. :-1.0000 Min. :-1.0000 Min. :-1.0000
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## Median :-0.9836 Median :-0.9970 Median :-0.9955 Median :-0.9919
## Mean :-0.9094 Mean :-0.9374 Mean :-0.9517 Mean :-0.9393
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## attr343 attr344 attr345 attr346
## Min. :-1.0000 Min. :-1.0000 Min. :-1.0000 Min. :-1.0000
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## Median :-0.9833 Median :-0.9970 Median :-0.9382 Median :-0.9041
## Mean :-0.9015 Mean :-0.9580 Mean :-0.6647 Mean :-0.6323
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## attr347 attr348 attr349 attr350
## Min. :-1.0000 Min. :-1.0000 Min. :-1.0000 Min. :-1.0000
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## Median :-0.9316 Median :-0.9435 Median :-0.9086 Median :-0.9464
## Mean :-0.7422 Mean :-0.6657 Mean :-0.6169 Mean :-0.7800
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## Max. : 1.0000 Max. : 1.0000 Max. : 1.0000 Max. : 1.0000
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## attr351 attr352 attr353 attr354
## Min. :-1.0000 Min. :-1.0000 Min. :-1.0000 Min. :-1.0000
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## Median :-0.9294 Median :-0.9085 Median :-0.9416 Median :-0.9581
## Mean :-0.6067 Mean :-0.6288 Mean :-0.7642 Mean :-0.7212
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## attr355 attr356 attr357 attr358
## Min. :-1.0000 Min. :-1.0000 Min. :-1.0000 Min. :-1.0000
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## Median :-0.9273 Median :-0.9522 Median :-0.9815 Median :-0.9683
## Mean :-0.6842 Mean :-0.8002 Mean :-0.8837 Mean :-0.8623
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## Max. : 1.0000 Max. : 1.0000 Max. : 1.0000 Max. : 1.0000
##
## attr359 attr360 attr361 attr362
## Min. :-1.0000 Min. :-1.0000 Min. :-1.0000 Min. :-1.0000
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## Median :-0.9683 Median :-0.9149 Median :-0.9977 Median :-0.9944
## Mean :-0.8838 Mean :-0.6250 Mean :-0.8561 Mean :-0.8328
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## attr363 attr364 attr365 attr366
## Min. :-1.0000 Min. :-1.0000 Min. :-1.0000 Min. :-1.0000
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## Median :-0.9973 Median :-0.9285 Median :-0.9280 Median :-0.9385
## Mean :-0.9297 Mean :-0.6411 Mean :-0.7224 Mean :-0.7696
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## attr367 attr368 attr369 attr370
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## Median :-0.5844 Median :-0.5302 Median :-0.5844 Median :-0.4000
## Mean :-0.2673 Mean :-0.2576 Mean :-0.3587 Mean :-0.4191
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## Max. : 1.0000 Max. : 0.9968 Max. : 1.0000 Max. : 1.0000
##
## attr371 attr372 attr373 attr374
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## Median :-0.4000 Median :-0.320 Median :-0.14740 Median :-0.22124
## Mean :-0.4033 Mean :-0.341 Mean :-0.13956 Mean :-0.19676
## 3rd Qu.:-0.2400 3rd Qu.:-0.160 3rd Qu.: 0.08637 3rd Qu.: 0.01976
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##
## attr375 attr376 attr377 attr378
## Min. :-1.00000 Min. :-1.0000 Min. :-0.9956 Min. :-1.0000
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## Median : 0.03306 Median :-0.3747 Median :-0.7959 Median :-0.4763
## Mean : 0.01899 Mean :-0.3359 Mean :-0.7340 Mean :-0.4533
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## attr379 attr380 attr381 attr382
## Min. :-1.0000 Min. :-0.9548 Min. :-1.0000 Min. :-1.0000
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## Median :-0.8581 Median :-0.4986 Median :-0.8658 Median :-0.9992
## Mean :-0.8216 Mean :-0.4653 Mean :-0.8253 Mean :-0.8685
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## Max. : 1.0000 Max. : 1.0000 Max. : 1.0000 Max. : 1.0000
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## attr383 attr384 attr385 attr386
## Min. :-1.0000 Min. :-1.0000 Min. :-1.0000 Min. :-1.0000
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## Median :-0.9986 Median :-0.9978 Median :-0.9975 Median :-0.9983
## Mean :-0.8937 Mean :-0.8794 Mean :-0.9036 Mean :-0.9238
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## attr387 attr388 attr389 attr390
## Min. :-1.0000 Min. :-1.0000 Min. :-1.0000 Min. :-1.0000
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## Median :-0.9981 Median :-0.9988 Median :-0.9999 Median :-0.9987
## Mean :-0.9051 Mean :-0.9463 Mean :-0.9847 Mean :-0.8731
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## Max. : 1.0000 Max. : 1.0000 Max. : 1.0000 Max. : 1.0000
##
## attr391 attr392 attr393 attr394
## Min. :-1.0000 Min. :-1.0000 Min. :-1.0000 Min. :-1.0000
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## Median :-0.9972 Median :-0.9981 Median :-0.9988 Median :-0.9980
## Mean :-0.8619 Mean :-0.9098 Mean :-0.9443 Mean :-0.8522
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## Max. : 1.0000 Max. : 1.0000 Max. : 1.0000 Max. : 1.0000
##
## attr395 attr396 attr397 attr398
## Min. :-1.0000 Min. :-1.0000 Min. :-1.0000 Min. :-1.0000
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## Median :-0.9967 Median :-0.9913 Median :-0.9964 Median :-0.9959
## Mean :-0.8682 Mean :-0.8407 Mean :-0.8713 Mean :-0.8438
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##
## attr399 attr400 attr401 attr402
## Min. :-1.0000 Min. :-1.0000 Min. :-1.0000 Min. :-1.0000
## 1st Qu.:-0.9998 1st Qu.:-0.9997 1st Qu.:-0.9996 1st Qu.:-0.9997
## Median :-0.9971 Median :-0.9970 Median :-0.9950 Median :-0.9969
## Mean :-0.9124 Mean :-0.9174 Mean :-0.8789 Mean :-0.9243
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## attr403 attr404 attr405 attr406
## Min. :-1.0000 Min. :-1.0000 Min. :-1.0000 Min. :-1.0000
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## Median :-0.9995 Median :-0.9943 Median :-0.9955 Median :-0.9954
## Mean :-0.9719 Mean :-0.8458 Mean :-0.8447 Mean :-0.8811
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## Max. : 1.0000 Max. : 0.8979 Max. : 0.9303 Max. : 1.0000
##
## attr407 attr408 attr409 attr410
## Min. :-1.0000 Min. :-1.0000 Min. :-1.0000 Min. :-1.0000
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## Median :-0.9971 Median :-0.9942 Median :-0.9963 Median :-0.9943
## Mean :-0.9303 Mean :-0.8190 Mean :-0.8992 Mean :-0.8983
## 3rd Qu.:-0.9011 3rd Qu.:-0.6850 3rd Qu.:-0.8445 3rd Qu.:-0.8609
## Max. : 1.0000 Max. : 0.9149 Max. : 0.8074 Max. : 1.0000
##
## attr411 attr412 attr413 attr414
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## 1st Qu.:-0.9997 1st Qu.:-0.9998 1st Qu.:-0.9998 1st Qu.:-0.9997
## Median :-0.9963 Median :-0.9982 Median :-0.9987 Median :-0.9985
## Mean :-0.8995 Mean :-0.9306 Mean :-0.9623 Mean :-0.9661
## 3rd Qu.:-0.8632 3rd Qu.:-0.9186 3rd Qu.:-0.9579 3rd Qu.:-0.9616
## Max. : 1.0000 Max. : 1.0000 Max. : 1.0000 Max. : 1.0000
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## attr415 attr416 attr417 attr418
## Min. :-1.0000 Min. :-1.0000 Min. :-1.0000 Min. :-1.0000
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## Median :-0.9970 Median :-0.9965 Median :-0.9993 Median :-0.9945
## Mean :-0.9403 Mean :-0.9312 Mean :-0.9705 Mean :-0.8779
## 3rd Qu.:-0.9273 3rd Qu.:-0.9189 3rd Qu.:-0.9872 3rd Qu.:-0.8216
## Max. : 1.0000 Max. : 1.0000 Max. : 1.0000 Max. : 1.0000
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## attr419 attr420 attr421 attr422
## Min. :-1.0000 Min. :-1.0000 Min. :-1.0000 Min. :-1.0000
## 1st Qu.:-0.9998 1st Qu.:-0.9997 1st Qu.:-0.9995 1st Qu.:-0.9997
## Median :-0.9984 Median :-0.9980 Median :-0.9965 Median :-0.9963
## Mean :-0.9461 Mean :-0.9561 Mean :-0.9314 Mean :-0.8984
## 3rd Qu.:-0.9338 3rd Qu.:-0.9464 3rd Qu.:-0.9186 3rd Qu.:-0.8530
## Max. : 1.0000 Max. : 1.0000 Max. : 1.0000 Max. : 1.0000
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## attr423 attr424 attr425 attr426
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## Median :-0.9984 Median :-0.8496 Median :-0.8921 Median :-0.8547
## Mean :-0.9599 Mean :-0.6638 Mean :-0.6969 Mean :-0.6337
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## attr427 attr428 attr429 attr430
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## Median :-0.8658 Median :-0.8739 Median :-0.8789 Median :-0.8567
## Mean :-0.7248 Mean :-0.6517 Mean :-0.7243 Mean :-0.6976
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## Median :-0.8910 Median :-0.8574 Median :-0.8813 Median :-0.8943
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## Median :-0.8864 Median :-0.9795 Median :-0.9707 Median :-0.9662
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## Median :-0.8630 Median :-0.9901 Median :-0.9925 Median :-0.9906
## Mean :-0.6504 Mean :-0.9092 Mean :-0.8748 Mean :-0.8969
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## Median :-0.9050 Median :-0.9226 Median :-0.9118 Median :-0.06708
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## Median :-0.9908 Median :-0.9958 Median :-0.9972 Median :-0.9979
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## Median :-0.9968 Median :-0.9965 Median :-0.9970 Median :-0.9993
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## Median :-0.9903 Median :-0.9967 Median :-0.9963 Median :-0.9974
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## Median :-0.9902 Median :-0.9973 Median :-0.9919 Median :-0.9982
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## Median :-0.9776 Median :-0.8970 Median :-0.2116 Median :-0.8947
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## Median : 0.07336 Median :-0.4081 Median :-0.7171 Median :-0.9082
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## Mean :-0.6501 Mean :-0.6222 Mean :-0.6949 Mean :-0.8079
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## Max. : 1.0000 Max. : 1.0000 Max. : 1.0000 Max. : 1.0000
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## Median :-0.9082 Median :-0.9945 Median :-0.9237 Median :-0.5539
## Mean :-0.6273 Mean :-0.8472 Mean :-0.6817 Mean :-0.3364
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## Max. : 1.0000 Max. : 1.0000 Max. : 1.0000 Max. : 1.0000
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## Mean :-0.7267 Mean :-0.8833 Mean :-0.6843 Mean :-0.8654
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## 0 02.a.vi) Summarize the levels of the class attribute.
cbind(freq=table(y_train), percentage=prop.table(table(y_train))*100)## freq percentage
## 1 1226 15.7847303
## 2 1073 13.8148577
## 3 987 12.7076091
## 4 1293 16.6473542
## 5 1423 18.3211021
## 6 1413 18.1923523
## 7 47 0.6051242
## 8 23 0.2961246
## 9 75 0.9656238
## 10 60 0.7724990
## 11 90 1.1587486
## 12 57 0.73387412.b) Data visualizations
2.b.i) Univariate plots to better understand each attribute.
# Boxplots for each attribute
# par(mfrow=c(dispRow,dispCol))
for(i in 1:totAttr) {
boxplot(x_train[,i], main=names(x_train)[i])
}
# Histograms each attribute
# par(mfrow=c(dispRow,dispCol))
for(i in 1:totAttr) {
hist(x_train[,i], main=names(x_train)[i])
}
# Density plot for each attribute
# par(mfrow=c(dispRow,dispCol))
for(i in 1:totAttr) {
plot(density(x_train[,i]), main=names(x_train)[i])
}
2.b.ii) Multivariate plots to better understand the relationships between attributes
# Scatterplot matrix colored by class
# pairs(targetVar~., data=xy_train, col=xy_train$targetVar)# Box and whisker plots for each attribute by class
# scales <- list(x=list(relation="free"), y=list(relation="free"))
# featurePlot(x=x_train, y=y_train, plot="box", scales=scales)# Density plots for each attribute by class value
# featurePlot(x=x_train, y=y_train, plot="density", scales=scales)# Correlation plot
correlations <- cor(x_train)
corrplot(correlations, method="circle")
email_notify(paste("Data Summarization and Visualization completed!",date()))## [1] "Java-Object{org.apache.commons.mail.SimpleEmail@6fc6f14e}"3. Prepare Data
Some dataset may require additional preparation activities that will best exposes the structure of the problem and the relationships between the input attributes and the output variable. Some data-prep tasks might include:
- Cleaning data by removing duplicates, marking missing values and even imputing missing values.
- Feature selection where redundant features may be removed.
- Data transforms where attributes are scaled or redistributed in order to best expose the structure of the problem later to learning algorithms.
email_notify(paste("Data Cleaning and Transformation has begun!",date()))## [1] "Java-Object{org.apache.commons.mail.SimpleEmail@6d7b4f4c}"3.a) Data Cleaning
# Not applicable for this iteration of the project3.b) Feature Selection
# Using the correlations calculated previously, we try to find attributes that are highly correlated.
highlyCorrelated <- findCorrelation(correlations, cutoff=0.99)
print(highlyCorrelated)## [1] 67 89 168 169 201 206 214 215 219 240 242 245 255 311 312 315 326
## [18] 329 343 345 346 347 351 352 353 360 407 412 430 473 488 501 516 518
## [35] 521 524 542 544 547 4 5 6 44 45 46 41 70 71 74 75 76
## [52] 84 85 124 125 126 164 202 203 204 205 207 208 209 210 211 212 213
## [69] 96 228 227 229 176 253 7 8 9 266 267 282 283 284 87 88 86
## [86] 97 98 99 388 361 319 362 334 416 127 128 129 138 440 441 442 216
## [103] 503 241 529 254 42 43cat('Number of attributes found to be highly correlated:',length(highlyCorrelated))## Number of attributes found to be highly correlated: 108# Removing the highly correlated attributes from the training and validation dataframes
xy_train <- xy_train[, -highlyCorrelated]
xy_test <- xy_test[, -highlyCorrelated]3.c) Data Transforms
# Not applicable for this iteration of the project3.d) Display the Final Dataset for Model-Building
dim(xy_train)## [1] 7767 454dim(xy_test)## [1] 3162 454sapply(xy_train, class)## attr1 attr2 attr3 attr10 attr11 attr12 attr13
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric"
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## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric"
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## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric"
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## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric"
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## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric"
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## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric"
## attr540 attr541 attr543 attr545 attr546 attr548 attr549
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric"
## attr550 attr551 attr552 attr553 attr554 attr555 attr556
## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric"
## attr557 attr558 attr559 attr560 attr561 targetVar
## "numeric" "numeric" "numeric" "numeric" "numeric" "factor"email_notify(paste("Data Cleaning and Transformation completed!",date()))## [1] "Java-Object{org.apache.commons.mail.SimpleEmail@63753b6d}"proc.time()-startTimeScript## user system elapsed
## 169.94 154.28 366.944. Model and Evaluate Algorithms
After the data-prep, we next work on finding a workable model by evaluating a subset of machine learning algorithms that are good at exploiting the structure of the training. The typical evaluation tasks include:
- Defining test options such as cross validation and the evaluation metric to use.
- Spot checking a suite of linear and nonlinear machine learning algorithms.
- Comparing the estimated accuracy of algorithms.
For this project, we will evaluate one linear, three non-linear, and three ensemble algorithms:
Linear Algorithm: Linear Discriminant Analysis
Non-Linear Algorithms: Decision Trees (CART) and k-Nearest Neighbors
Ensemble Algorithms: Bagged CART, Random Forest, and Stochastic Gradient Boosting
The random number seed is reset before each run to ensure that the evaluation of each algorithm is performed using the same data splits. It ensures the results are directly comparable.
4.a) Generate models using linear algorithms
# Linear Discriminant Analysis (Classification)
email_notify(paste("Linear Discriminant Analysis modeling has begun!",date()))## [1] "Java-Object{org.apache.commons.mail.SimpleEmail@6c3708b3}"startTimeModule <- proc.time()
set.seed(seedNum)
fit.lda <- train(targetVar~., data=xy_train, method="lda", metric=metricTarget, trControl=control)## Warning in lda.default(x, grouping, ...): variables are collinear
## Warning in lda.default(x, grouping, ...): variables are collinear
## Warning in lda.default(x, grouping, ...): variables are collinear
## Warning in lda.default(x, grouping, ...): variables are collinear
## Warning in lda.default(x, grouping, ...): variables are collinear
## Warning in lda.default(x, grouping, ...): variables are collinear
## Warning in lda.default(x, grouping, ...): variables are collinear
## Warning in lda.default(x, grouping, ...): variables are collinear
## Warning in lda.default(x, grouping, ...): variables are collinear
## Warning in lda.default(x, grouping, ...): variables are collinear
## Warning in lda.default(x, grouping, ...): variables are collinearprint(fit.lda)## Linear Discriminant Analysis
##
## 7767 samples
## 453 predictor
## 12 classes: '1', '2', '3', '4', '5', '6', '7', '8', '9', '10', '11', '12'
##
## No pre-processing
## Resampling: Cross-Validated (10 fold, repeated 1 times)
## Summary of sample sizes: 6990, 6988, 6992, 6993, 6992, 6989, ...
## Resampling results:
##
## Accuracy Kappa
## 0.9705206 0.9651129proc.time()-startTimeModule## user system elapsed
## 55.33 14.09 20.85email_notify(paste("Linear Discriminant Analysis modeling completed!",date()))## [1] "Java-Object{org.apache.commons.mail.SimpleEmail@57536d79}"4.b) Generate models using nonlinear algorithms
# Decision Tree - CART (Regression/Classification)
email_notify(paste("Decision Tree modeling has begun!",date()))## [1] "Java-Object{org.apache.commons.mail.SimpleEmail@1f28c152}"startTimeModule <- proc.time()
set.seed(seedNum)
fit.cart <- train(targetVar~., data=xy_train, method="rpart", metric=metricTarget, trControl=control)
print(fit.cart)## CART
##
## 7767 samples
## 453 predictor
## 12 classes: '1', '2', '3', '4', '5', '6', '7', '8', '9', '10', '11', '12'
##
## No pre-processing
## Resampling: Cross-Validated (10 fold, repeated 1 times)
## Summary of sample sizes: 6990, 6988, 6992, 6993, 6992, 6989, ...
## Resampling results across tuning parameters:
##
## cp Accuracy Kappa
## 0.1557377 0.5549245 0.46351732
## 0.1927806 0.4727254 0.36048507
## 0.2200504 0.2541464 0.08698281
##
## Accuracy was used to select the optimal model using the largest value.
## The final value used for the model was cp = 0.1557377.proc.time()-startTimeModule## user system elapsed
## 88.64 9.87 73.16email_notify(paste("Decision Tree modeling completed!",date()))## [1] "Java-Object{org.apache.commons.mail.SimpleEmail@67b92f0a}"# k-Nearest Neighbors (Regression/Classification)
email_notify(paste("k-Nearest Neighbors modeling has begun!",date()))## [1] "Java-Object{org.apache.commons.mail.SimpleEmail@887af79}"startTimeModule <- proc.time()
set.seed(seedNum)
fit.knn <- train(targetVar~., data=xy_train, method="knn", metric=metricTarget, trControl=control)
print(fit.knn)## k-Nearest Neighbors
##
## 7767 samples
## 453 predictor
## 12 classes: '1', '2', '3', '4', '5', '6', '7', '8', '9', '10', '11', '12'
##
## No pre-processing
## Resampling: Cross-Validated (10 fold, repeated 1 times)
## Summary of sample sizes: 6990, 6988, 6992, 6993, 6992, 6989, ...
## Resampling results across tuning parameters:
##
## k Accuracy Kappa
## 5 0.9524956 0.9437625
## 7 0.9496635 0.9404043
## 9 0.9501795 0.9410091
##
## Accuracy was used to select the optimal model using the largest value.
## The final value used for the model was k = 5.proc.time()-startTimeModule## user system elapsed
## 1343.75 0.74 1351.59email_notify(paste("k-Nearest Neighbors modeling completed!",date()))## [1] "Java-Object{org.apache.commons.mail.SimpleEmail@23e028a9}"4.c) Generate models using ensemble algorithms
In this section, we will explore the use and tuning of ensemble algorithms to see whether we can improve the results.
# Bagged CART (Regression/Classification)
email_notify(paste("Bagged CART modeling has begun!",date()))## [1] "Java-Object{org.apache.commons.mail.SimpleEmail@3701eaf6}"startTimeModule <- proc.time()
set.seed(seedNum)
fit.bagcart <- train(targetVar~., data=xy_train, method="treebag", metric=metricTarget, trControl=control)
print(fit.bagcart)## Bagged CART
##
## 7767 samples
## 453 predictor
## 12 classes: '1', '2', '3', '4', '5', '6', '7', '8', '9', '10', '11', '12'
##
## No pre-processing
## Resampling: Cross-Validated (10 fold, repeated 1 times)
## Summary of sample sizes: 6990, 6988, 6992, 6993, 6992, 6989, ...
## Resampling results:
##
## Accuracy Kappa
## 0.9573827 0.9495514proc.time()-startTimeModule## user system elapsed
## 1738.21 319.86 1176.03email_notify(paste("Bagged CART modeling completed!",date()))## [1] "Java-Object{org.apache.commons.mail.SimpleEmail@551aa95a}"# Random Forest (Regression/Classification)
email_notify(paste("Random Forest modeling has begun!",date()))## [1] "Java-Object{org.apache.commons.mail.SimpleEmail@3cef309d}"startTimeModule <- proc.time()
set.seed(seedNum)
fit.rf <- train(targetVar~., data=xy_train, method="rf", metric=metricTarget, trControl=control)
print(fit.rf)## Random Forest
##
## 7767 samples
## 453 predictor
## 12 classes: '1', '2', '3', '4', '5', '6', '7', '8', '9', '10', '11', '12'
##
## No pre-processing
## Resampling: Cross-Validated (10 fold, repeated 1 times)
## Summary of sample sizes: 6990, 6988, 6992, 6993, 6992, 6989, ...
## Resampling results across tuning parameters:
##
## mtry Accuracy Kappa
## 2 0.9518508 0.9429537
## 227 0.9681960 0.9623539
## 453 0.9617590 0.9547282
##
## Accuracy was used to select the optimal model using the largest value.
## The final value used for the model was mtry = 227.proc.time()-startTimeModule## user system elapsed
## 6585.00 0.93 6619.40email_notify(paste("Random Forest modeling completed!",date()))## [1] "Java-Object{org.apache.commons.mail.SimpleEmail@7494e528}"# Stochastic Gradient Boosting (Regression/Classification)
email_notify(paste("Stochastic Gradient Boosting modeling has begun!",date()))## [1] "Java-Object{org.apache.commons.mail.SimpleEmail@5e853265}"startTimeModule <- proc.time()
set.seed(seedNum)
fit.gbm <- train(targetVar~., data=xy_train, method="gbm", metric=metricTarget, trControl=control, verbose=F)
print(fit.gbm)## Stochastic Gradient Boosting
##
## 7767 samples
## 453 predictor
## 12 classes: '1', '2', '3', '4', '5', '6', '7', '8', '9', '10', '11', '12'
##
## No pre-processing
## Resampling: Cross-Validated (10 fold, repeated 1 times)
## Summary of sample sizes: 6990, 6988, 6992, 6993, 6992, 6989, ...
## Resampling results across tuning parameters:
##
## interaction.depth n.trees Accuracy Kappa
## 1 50 0.9303393 0.9174535
## 1 100 0.9504272 0.9412809
## 1 150 0.9593121 0.9518173
## 2 50 0.9541569 0.9457053
## 2 100 0.9658736 0.9595851
## 2 150 0.9702533 0.9647733
## 3 50 0.9609840 0.9537980
## 3 100 0.9712842 0.9659935
## 3 150 0.9730882 0.9681269
##
## Tuning parameter 'shrinkage' was held constant at a value of 0.1
##
## Tuning parameter 'n.minobsinnode' was held constant at a value of 10
## Accuracy was used to select the optimal model using the largest value.
## The final values used for the model were n.trees = 150,
## interaction.depth = 3, shrinkage = 0.1 and n.minobsinnode = 10.proc.time()-startTimeModule## user system elapsed
## 5580.28 1.39 5611.36email_notify(paste("Stochastic Gradient Boosting modeling completed!",date()))## [1] "Java-Object{org.apache.commons.mail.SimpleEmail@1e6d1014}"4.d) Compare baseline algorithms
results <- resamples(list(LDA=fit.lda, CART=fit.cart, kNN=fit.knn, BagCART=fit.bagcart, RF=fit.rf, GBM=fit.gbm))
summary(results)##
## Call:
## summary.resamples(object = results)
##
## Models: LDA, CART, kNN, BagCART, RF, GBM
## Number of resamples: 10
##
## Accuracy
## Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
## LDA 0.9627249 0.9661963 0.9703591 0.9705206 0.9726694 0.9832041 0
## CART 0.5155039 0.5199614 0.5212082 0.5549245 0.6019210 0.6447876 0
## kNN 0.9447301 0.9488093 0.9511890 0.9524956 0.9580245 0.9601030 0
## BagCART 0.9535484 0.9543279 0.9568855 0.9573827 0.9596785 0.9626770 0
## RF 0.9612903 0.9645377 0.9684685 0.9681960 0.9711069 0.9768638 0
## GBM 0.9627249 0.9706164 0.9716494 0.9730882 0.9784427 0.9807198 0
##
## Kappa
## Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
## LDA 0.9559162 0.9599934 0.9649273 0.9651129 0.9676571 0.9801149 0
## CART 0.4155538 0.4205542 0.4226051 0.4635173 0.5206975 0.5730081 0
## kNN 0.9345629 0.9394042 0.9422239 0.9437625 0.9502767 0.9527861 0
## BagCART 0.9449711 0.9459949 0.9489542 0.9495514 0.9522539 0.9558024 0
## RF 0.9541918 0.9580087 0.9626630 0.9623539 0.9658218 0.9726105 0
## GBM 0.9558321 0.9651761 0.9664351 0.9681269 0.9744661 0.9771739 0dotplot(results)
cat('The average accuracy from all models is:',
mean(c(results$values$`LDA~Accuracy`,results$values$`CART~Accuracy`,results$values$`kNN~Accuracy`,results$values$`BagCART~Accuracy`,results$values$`RF~Accuracy`,results$values$`GBM~Accuracy`)))## The average accuracy from all models is: 0.89610135. Improve Accuracy or Results
After we achieve a short list of machine learning algorithms with good level of accuracy, we can leverage ways to improve the accuracy of the models.
Using the three best-perfoming algorithms from the previous section, we will Search for a combination of parameters for each algorithm that yields the best results.
5.a) Algorithm Tuning
Finally, we will tune the best-performing algorithms from each group further and see whether we can get more accuracy out of them.
# Tuning algorithm #1 - Linear Discriminant Analysis
# Linear Discriminant Analysis has no special tuning parameters
email_notify(paste("Algorithm #1 tuning has begun!",date()))## [1] "Java-Object{org.apache.commons.mail.SimpleEmail@131276c2}"startTimeModule <- proc.time()
set.seed(seedNum)
fit.final1 <- fit.lda
print(fit.final1)## Linear Discriminant Analysis
##
## 7767 samples
## 453 predictor
## 12 classes: '1', '2', '3', '4', '5', '6', '7', '8', '9', '10', '11', '12'
##
## No pre-processing
## Resampling: Cross-Validated (10 fold, repeated 1 times)
## Summary of sample sizes: 6990, 6988, 6992, 6993, 6992, 6989, ...
## Resampling results:
##
## Accuracy Kappa
## 0.9705206 0.9651129proc.time()-startTimeModule## user system elapsed
## 0 0 0email_notify(paste("Algorithm #1 tuning completed!",date()))## [1] "Java-Object{org.apache.commons.mail.SimpleEmail@51cdd8a}"# Tuning algorithm #2 - Stochastic Gradient Boosting
email_notify(paste("Algorithm #2 tuning has begun!",date()))## [1] "Java-Object{org.apache.commons.mail.SimpleEmail@10bbd20a}"startTimeModule <- proc.time()
set.seed(seedNum)
grid <- expand.grid(.n.trees=c(200,350,500), .shrinkage=0.1, .interaction.depth=3, .n.minobsinnode=10)
fit.final2 <- train(targetVar~., data=xy_train, method="gbm", metric=metricTarget, tuneGrid=grid, trControl=control, verbose=F)
plot(fit.final2)
print(fit.final2)## Stochastic Gradient Boosting
##
## 7767 samples
## 453 predictor
## 12 classes: '1', '2', '3', '4', '5', '6', '7', '8', '9', '10', '11', '12'
##
## No pre-processing
## Resampling: Cross-Validated (10 fold, repeated 1 times)
## Summary of sample sizes: 6990, 6988, 6992, 6993, 6992, 6989, ...
## Resampling results across tuning parameters:
##
## n.trees Accuracy Kappa
## 200 0.9761806 0.9717867
## 350 0.9770797 0.9728532
## 500 0.9769523 0.9727017
##
## Tuning parameter 'interaction.depth' was held constant at a value of
## 3
## Tuning parameter 'shrinkage' was held constant at a value of 0.1
##
## Tuning parameter 'n.minobsinnode' was held constant at a value of 10
## Accuracy was used to select the optimal model using the largest value.
## The final values used for the model were n.trees = 350,
## interaction.depth = 3, shrinkage = 0.1 and n.minobsinnode = 10.proc.time()-startTimeModule## user system elapsed
## 9155.45 1.28 9158.06email_notify(paste("Algorithm #2 tuning completed!",date()))## [1] "Java-Object{org.apache.commons.mail.SimpleEmail@5a1c0542}"5.d) Compare Algorithms After Tuning
results <- resamples(list(LDA=fit.final1, GBM=fit.final2))
summary(results)##
## Call:
## summary.resamples(object = results)
##
## Models: LDA, GBM
## Number of resamples: 10
##
## Accuracy
## Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
## LDA 0.9627249 0.9661963 0.9703591 0.9705206 0.9726694 0.9832041 0
## GBM 0.9717224 0.9729730 0.9754839 0.9770797 0.9800489 0.9871630 0
##
## Kappa
## Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
## LDA 0.9559162 0.9599934 0.9649273 0.9651129 0.9676571 0.9801149 0
## GBM 0.9664995 0.9680025 0.9709543 0.9728532 0.9763719 0.9848060 0dotplot(results)
6. Finalize Model and Present Results
Once we have narrow down to a model that we believe can make accurate predictions on unseen data, we are ready to finalize it. Finalizing a model may involve sub-tasks such as:
- Using an optimal model tuned to make predictions on unseen data.
- Creating a standalone model using the tuned parameters
- Saving an optimal model to file for later use.
email_notify(paste("Model Validation and Final Model Creation has begun!",date()))## [1] "Java-Object{org.apache.commons.mail.SimpleEmail@167fdd33}"6.a) Predictions on validation dataset
predictions <- predict(fit.final2, newdata=x_test)
confusionMatrix(predictions, y_test$targetVar)## Confusion Matrix and Statistics
##
## Reference
## Prediction 1 2 3 4 5 6 7 8 9 10 11 12
## 1 484 26 6 0 0 0 0 0 0 0 2 1
## 2 11 439 25 0 0 0 4 0 0 0 1 1
## 3 1 3 388 0 0 0 0 0 0 0 0 0
## 4 0 1 0 447 35 0 1 1 1 1 5 0
## 5 0 2 1 59 520 0 2 0 0 0 1 1
## 6 0 0 0 0 0 545 0 0 0 0 0 0
## 7 0 0 0 2 0 0 13 2 1 0 1 1
## 8 0 0 0 0 1 0 0 7 0 0 0 0
## 9 0 0 0 0 0 0 2 0 26 0 6 0
## 10 0 0 0 0 0 0 0 0 0 15 0 4
## 11 0 0 0 0 0 0 1 0 4 0 33 0
## 12 0 0 0 0 0 0 0 0 0 9 0 19
##
## Overall Statistics
##
## Accuracy : 0.9285
## 95% CI : (0.919, 0.9373)
## No Information Rate : 0.1758
## P-Value [Acc > NIR] : < 2.2e-16
##
## Kappa : 0.9157
## Mcnemar's Test P-Value : NA
##
## Statistics by Class:
##
## Class: 1 Class: 2 Class: 3 Class: 4 Class: 5 Class: 6
## Sensitivity 0.9758 0.9321 0.9238 0.8799 0.9353 1.0000
## Specificity 0.9869 0.9844 0.9985 0.9830 0.9747 1.0000
## Pos Pred Value 0.9326 0.9127 0.9898 0.9085 0.8874 1.0000
## Neg Pred Value 0.9955 0.9881 0.9884 0.9772 0.9860 1.0000
## Prevalence 0.1569 0.1490 0.1328 0.1607 0.1758 0.1724
## Detection Rate 0.1531 0.1388 0.1227 0.1414 0.1645 0.1724
## Detection Prevalence 0.1641 0.1521 0.1240 0.1556 0.1853 0.1724
## Balanced Accuracy 0.9813 0.9582 0.9612 0.9315 0.9550 1.0000
## Class: 7 Class: 8 Class: 9 Class: 10 Class: 11
## Sensitivity 0.565217 0.700000 0.812500 0.600000 0.67347
## Specificity 0.997770 0.999683 0.997444 0.998725 0.99839
## Pos Pred Value 0.650000 0.875000 0.764706 0.789474 0.86842
## Neg Pred Value 0.996817 0.999049 0.998082 0.996818 0.99488
## Prevalence 0.007274 0.003163 0.010120 0.007906 0.01550
## Detection Rate 0.004111 0.002214 0.008223 0.004744 0.01044
## Detection Prevalence 0.006325 0.002530 0.010753 0.006009 0.01202
## Balanced Accuracy 0.781494 0.849841 0.904972 0.799362 0.83593
## Class: 12
## Sensitivity 0.703704
## Specificity 0.997129
## Pos Pred Value 0.678571
## Neg Pred Value 0.997447
## Prevalence 0.008539
## Detection Rate 0.006009
## Detection Prevalence 0.008855
## Balanced Accuracy 0.8504166.b) Create standalone model on entire training dataset
startTimeModule <- proc.time()
library(gbm)## Loading required package: survival##
## Attaching package: 'survival'## The following object is masked from 'package:caret':
##
## cluster## Loading required package: splines## Loading required package: parallel## Loaded gbm 2.1.3set.seed(seedNum)
# Combining the training and test datasets to form the original dataset that will be used for training the final model
#xy_complete <- rbind(xy_train, xy_test)
#finalModel <- gbm(targetVar~., xy_train, n.trees=350, shrinkage=0.1, interaction.depth=3, n.minobsinnode=1)
#summary(finalModel)
proc.time()-startTimeModule## user system elapsed
## 0.03 0.00 0.036.c) Save model for later use
#saveRDS(finalModel, "./finalModel_MultiClass.rds")email_notify(paste("Model Validation and Final Model Creation Completed!",date()))## [1] "Java-Object{org.apache.commons.mail.SimpleEmail@74650e52}"proc.time()-startTimeScript## user system elapsed
## 24723.34 502.92 24489.00